Sven

Use 1JZ vvti trigger mode, offset should be close to zero with that but you need to confirm with a timing light.  
Since you have an idle valve, you will need Equation load source set to MAP and the MAP sensor connected to the same manifold so that the ecu can compensate for the varying air volume passing through the idle valve.  
Turn off CLL until fuel table is tuned.
Turn on Async injection with min async PW = 1.0ms.  And put something like 5 in your accel sens table.  
Assuming it is NA, change your lambda target table so that 0.87 is the smallest value in there (WOT).  I normally have around 095 at idle, 0.9 at 40% TP and 0.87 at WOT. 
For your ign table copy your 60%TP row down to the 100% row, even then it will be on the conservative side.
Also, not related to your running problem, but I would suggest taking a whole lot of rows out of your fuel and ign tables, you are only creating a lot of tuning work by having so many.  For ITB's I usually do TP 0%,2,5,8,11,15,20,30,40,60,100.  Only add extra cells if there is found to be some area that is not taken care of by linear interpolation during tuning.  

Regarding Lambda control error correction table. I spend alot of time to tune these. The base map is adjusted the wrong way around. Because the error correction tables is a % corretion of actual error, you want big corrections like 15%  on small errors (0.03 lambda error) and small correction (like 5%) at the biggest error on the table. This is because a fuel film built up first in the ports when big correction are applied. This means it needs several burn cycles to get the whole change applied and measured. This means lambda control applies big changes two or three times for big corrections which leads to Lambda oscillation.  On small changes fuel film built up is much less.  Lambda change is done and measured much faster and within same burn cycle. This means the Lambda correction can be set much higher, because the change in AFR is measured instant.
I have attached a tuned example.  

For ITB's NA you will want your fuel & Ignition table Y axis to be throttle position, with very fine breakpoints for the first 10% or so of throttle movement.  I will attach below a fuel and ign table from an ITB engine that will be better starting points.  You can right click on your existing fuel or ign table and chose import/export>import from file.
Next, air flow balance or sync is very important for decent low speed running with ITB's, have you checked airflow is well balanced with a synchrometer or stethoscope etc? I cant see in the photo if there is adjustment between the individual blades or not.
ITB Ignition Table 1.lte ITB with MAP comp Fuel Table 1.lte

Also I noticed you dont have accel enrichment enabled.  You typically need plenty of this with ITB's.  
Looking through some of my files they seem to vary greatly, but below will be an average starting point.  I have some files with 3x this amount of enrichment...

Many thanks Adam, the 5l engine has a 347 stroker kit, the firing order is 351  as per custom cam grind specs,  traction control noted. FP noted.
yes ITB's, 48mm, home made when I had a bit of spare time a few years ago,  will set the arming threshold in the morning and see what happens

Ok, no signs of trigger error in your log but it wouldnt hurt to bump that trig 2 arming threshold up to something more relevant.
No other obvious signs of an issue in your log.
A couple of comments after looking at your tune:
Are you 100% sure your engine is using the "351/HO" firing order?  I know from a previous case that some 5.0's use the older 289/302 firing order. Turn traction control off for now.  It is not interfering in the log but with the slip aim at zero, it is going to start cutting as soon as the wheels start to turn. Set fuel system type to FP sensor since you have one, it will mean your tune is going to change but it will make your VE more realistic, make tuning easier and give you an extra layer of safety if fuel pressure ever drops.  Looking at your Avatar - does this engine have ITB's?

You would want to set the trig 2 arming threshold so that it is above that noise level, but otherwise it looks quite usable, provided it doesnt get exponentially worse at higher RPM etc.
In that scope capture your trig 2 waveform is about 6V high and the noise is about 0.5V.  So if you set the arming threshold for that specific RPM to say 3V, then the ECU will ignore everything below 3V.  
Are you getting trigger errors reported or any other trigger error symptoms such as RPM jumping around?
What coils does it have?  Do you have ignitors?
If you want to attach a short log of it running and the tune file I will take a look.
 

I my car I run an 11 position rotary switch to adjust traction control,
I prefer the switch rather than just a potentiometer as I can see and feel the adjustments on the go.
I run the output to a AN Volt INPUT and run a 3d allocation table.
I did this as I had no idea what slip % to start with and could try a wider range of settings on the go.
After playing I now have it setup at 9% slip in mid position and a difference of 1% per click.
I find it works quite well.
 
 

You can work out the polarity relatively easy with a volt meter. 
Put the leads across the sensor and then bring a steal ruler or bolt up to and then past the sensor. You are looking for a positive voltage spike as the item come towards the sensor and then negative as it moves away. 
If it is reversed then swap the meter leads over. 
The positive meter lead then indicates the trigger pin and the other is the sensor ground. 

I'm using these. http://www.kasensors.com/sites/default/files/downloads/SP08 Wheel Speed 10.18.pdf

AVSS is what the wire is not ADSS.
http://prd.sws.co.jp/cables/en/avss.html