Adamw

There are two different functions going on - 1) triggering to determine crank position and phase.  2) measurement and control of the VVT cam position relative to crank.
The cam pulse window is part of the triggering strategy - it means the ECU will only look for one tooth on the cam within a specific crank angular range so it can determine what phase the engine is in (Exhaust or compression stroke).  Effectively ignores the other two teeth so it only sees one unique event every 720  deg.
The cam pulse window is only used for the triggering, all 3 teeth on the cam are used to measure the cam position for the VVT control.  

Ah I missed it earlier but I now see a potential issue.  Your MAP limit table is a bit messed up so you are getting an 80% fuel cut when cranking.  
Attached to this post is a new copy of the MAP limit table from our RX7 base map.  If you go to your existing MAP limit table, right click, then import/export>import from file and choose this file below.  
MAP Limit Table 1.lte

Correct.
 
You can shorten the tooth (b1) down to the pole diameter (3.5mm on the drawing), so you can pick up a little space there.  I wouldnt want the gaps (b2) to be shorter than the teeth (b1), so if you cant achieve the diameter you want with the teeth and gaps no less than 3.5mm long then you would be best to reduce tooth count or find a sensor with a smaller pole.   
 
Not too critical, I like to place it outside of the normal range of ign timing so 60BTDC or 60ATDC is a good option on a 6cyl.
 
It is not critical, the trigger offset is set in the software when the engine is running. 
 
You can just use the 3 teeth on the HKS cam as both your sync (phase) and VVT position, you dont need a separate sync sensor.  This would use the "Cam window" sync option.  

All of the japanese performance ecu's of that era were just the factory ECU with a modified ROM.  Usually only minor changes from stock such as scaling for larger injectors and increase of RPM and boost limits.  

There are base maps in PC Link that will allow the engine to start and run with minimal set up, but it will need proper tuning before it can be driven hard.

Yeah, would likely work with 1JZ trigger mode.  If not the generic multitooth/missing mode with the cam window sync method will handle that.  VVT will be fine.

7K narrow will see that.  
However, just for your interest, I rarely find the calculated frequency is ideal.   Below is a pic from me doing some testing on our EJ207.  The calculated frequency based on the 92mm bore size for the engine would be about 6.2KHz.  
Frequency is on the Y axis of this pic.  If you look at 6.2K, there is so much noise it is hard to really see any difference between knock and no knock.  If you look at the 2nd harmonic of this at about 12.4K, it is not really any better.  In fact about 8-9KHz has the best signal to noise ratio for determining knock in this case.  
But what Im getting at is the bands are usually quite wide - +/-0.5KHz is not going to make much difference.  

No you can only send a numerical value over CAN.  You will have to ask Haltech to correct their dash firmware.  

Yep trailing split is normally negative for the FD engine.  Thats not going to stop it running though.  

Mostly looks ok to me.  I would lower the arming thresholds a bit to the examples below to make it a bit more robust but it looks like it has everything it needs to run.  Possibly plugs are fouled, rotaries can be a bit sensitive when the tune is a fair way out.  Looking at our FD map we have the master fuel at 14ms (has 850primaries) so perhaps drop yours to 12-14 so it doesnt have too much fuel dumping in there.    

 
Make sure you change that timing split table to negatives too.  

Rant time...
That is just innovate being innovate.  They used to also spit out the very robust NTK and LSU4.2 sensors at the same rate in the old days when they used to work with those sensors before the LSU 4.9 was even invented.  
They control the sensor completely differently than it was ever designed to be controlled so the controller is very sensitive to sensor response time.  The founder Klaus was a very smart guy that invented this new measurement strategy which gave very fast response and made control cheap/easy at a time (20years ago) when wideband controllers were a very expensive tuning tool not affordable for consumers.  You can read his patent here:  https://patents.google.com/patent/US6978655.   But when Klaus sold up shortly after the first LC1 was released their wideband controllers never got any improvements or fixes since.   Every innovate controller produced since is just a copy/paste and has the same issues the first ones had 20 years ago. As soon as the sensor ages a little or gets too hot or too cold, the innovate will report it as Error 2 or 8 and innovate will tell you the sensor has "failed".  It has not failed and will still work on any other LSU4.9 controller that uses proper control.  With Innovate controllers it is generally not thermal shock as per the NZEFI article.  So dont throw away any sensors the innovate tells you have "failed" until you try it on a non-innovate controller - 99% of them wont be failed. 
You can tell Im not a fan - my old boss used to have 8 of them on his engine dyno.  We used to go through 8 sensors about every 2 full dyno days there.   I still have a filing cabinet full of his "failed sensors" - I'll go through about 2 a year on my dyno - and that is usually only because I drop it. 
 
You certainly could, but if it is only 2-5% at low RPM I personally wouldnt bother.   
 
 
 

Hard to tell from your pic, but if it doesnt have a sensor on the upper wheel that has a single tooth and only has a sensor on the lower 4 tooth wheel then you need to set trigger 2 sync mode to none.  
1 wire to ground the other to trig 1.  

Yep it’s been in there a while now.  There is a set up guide and plumbing diagram in the help file.  

With the resistor in place the deadtimes will likely be quite wrong.  It wont be noticeable when everything is relatively stable as the deadtime error will just be "baked in" to the fuel map.  But if for example battery voltage changes (ie headlights of fan turns on) then the incorrect deadtimes arent going to compensate for that as well as they should.  If you remove the resistor you will likely need to retune the fuel table.  You wont do any damage to ecu or injector - just higher risk that all operating conditions wont be compensated for well.   

Most modern injectors will work down to a minimum effective PW of around 0.2ms.  

With no CAN the controller should switch the heater on after 15 seconds to try to protect the sensor.  So it should be at least pretty warm to the touch after 10mins.  So it suggests there is no power.
Can you check power supply by backprobing with pins or similar the Lambda side of the DTM4 connector - like my pic below.  I have for example seen some people assemble the DTM wrong so the terminals push back out and lose contact when you click the plug together.  
 

It uses the crank wheel for timing, but I wouldnt just trust that is correct as all manufacturers have engineering tolerances.  The offset will be close to zero on most.  My Evo VII offset is -1.  
If you are missing a timing mark then paint your own mark on.  

If the sweep is working then that would indicate the tacho is happy with the 12V pulse signal.  

You would likely see significant timing drift when performing the ign delay test during trigger calibration, and I would expect in logs and on screen etc at some points there would likely be significant dwell scatter.
 
 Depends what you mean by "melted".  Ign timing can cause knock - but this would usually break things rather than melt them.  Melting is generally pre-ignition which can be caused by lean mixtures or something "glowing" in the combustion chamber such as an incorrect heat range spark plug or wrong head gasket bore size etc
 
The "dwell time" is how how long you have the ign coil "turned on" for.  When the coil is "dwelling" the power you are feeding into it is being stored as a magnetic field.  Eventually this magnetic field reaches saturation (with an R8 coil it is around say 3ms).  Once it saturates then any further energy you put into it after that point is just making heat - it is not having any impact on the amount of energy stored in the coil.  The longer you have it "dwelling", also means there is less time between each dwell event to cool.  

With CAN plug at ecu end unplugged, but ign on and CAN lambda powered up (engine not running), is the sensor getting hot?

No twist wont have any effect when there is little electrical noise around.  
Can you give us a photo inside the back of the CANF connector.

"Limit Flags Word" is a good one to log also.  

Your Aux 5 E-throttle relay is off in that log.  Set "when stalled" mode to run.    

Evo's tend to do this in my experience, their sensor ground circuit must be connected to something that creates a variable ground offset.  Mine is 0.0% without the engine running and 0.2% with engine running.  
Just check the average TPS Delta runtime at idle then set your accel deadband above this so it doesnt trigger accel enrichment at idle.  

It certainly looks closer but there is still something wrong.  
The trigger 2 pattern should show 3 skinny slots every 90degs then a single wide slot in the 4th 90deg spot.  But you also have a weird group of 4 extra teeth just next to the wide slot and trig 1 signal gets a bit messed up at the same time.  
I have seen the Nissan CAS's do weird stuff like this if the voltage supply to them is very low (such as cranking on a flat battery).  So assuming the battery is good you may have to take another look at the CAS power supply.  You can also look at what the battery voltage is dropping to in a PC Link log while cranking to see if that is acceptable or not.