I was inspired a little, So went to my car started waited till idle stabilized at about 650 to 700 . The cam lopes a bit there, And admittingly on a flat but gravel drive. Placed in D4 the car lurched just a little and but didnt really move just kind of surged with the cam s rocked forward and back . though this was not my actual intent of experiment. I then placed it i rev which i would save with the lower numerical ratio should have moved less, But was also watching the TACH and realized the RPM in rev is almost 1000 rpm in addition a considerably higher line pressure is commanded and or caused by the rev boost valve , So I had a slight down surge idle then a quick jump to 1000 rpm and indeed the car does move move / pull more in reverse than drive idle.
I assume due to the higher idle speed though higher line might also affect converter operation, I did this as this part of the conversation interested me. But it seems the idle jumps a little I suppose to compensate for the energy requirements for the higher line in reverse?
I also went across the street and did the same the only thing that changed was with the surge of the cam 600 to 750 rpm it did slowly get the car moving every so slowly forward with each surge move it more.
Just some observations with my own car. Now bear in mind my car has a small torque cam and will idle quiet low while others with large cams would likely be much higher,
I also check my stock BIM seems factory desired idle on my car is 1000 rpm. I keep it lower as i like the semi choppy sound of the cam.
Just curious observations I just made.

 

Idle speed is the same (550rpm) for Drive and Reverse in the stock LS1 F-body tune. Mine always pulled similarly in either direction; a definite pull on level ground as soon as the brake pedal was released. That was with various Yank and PI converters of stall speeds equal to or greater than the OP's model. Once I put a cam in mine, I bumped the idle to 800rpm so I don't know how it would have behaved at the stock (lower) idle speed with a bigger cam and those same converters, but it sounds like the OP has a stock cam.

 

I only have my 1995 impala ss to use for comparison, I did think it odd the stock BIN showed a warm desired idle speed of 1000 rpm in gear PRND321 Rev had setting of it own and is still 1000 which I assume it bumped up . But in any case be it that or other reason it did indeed pull harder for sure in reverse than forward gears which surprised me really and the engagement is also much firmer even before the idle jumps but I would assume that is due to the considerable sudden increase of line pressure in reverse.I am a trans guy not a converter guy and do not pretend to have a more than elementary grasp of it all when it come to that. My greatest understanding is of how lockup works which in and of itself is much more complex that a simple apply with a DRUM/PISTON/CLUTCH apply and it has both apply and release oil .
Would greater line increase the pull I don't really know. Thicker oil as the OP mentioned certainly would. It would also slow clutch engagement assuming no leaks and proper regulation as thicker oil would slow the flow through the various orifices just as thinner would be quicker.
In my own car with an FTI 2800 TRIPLE DISC. at 650 to 700 rpm surging back and forth as it does I get no to moderate pull in D4 But certainly no hard pull and what little they is takes very little to stop or even a slight grade or bump. In rev however wither it the line increase or the RPM jump or both I am not sure. But it does indeed pull much more.
Just out of curiosity next time I have laptop plugged in I will command a higher line in D4 at idle and see just what does happen in this area.

Though hopefully soon I will be joining the HPTUNERS family as i am doing a 24x swap next month as I am tired of having such hard time getting a tune, asking for help with fuel tables I really do not understand with and competence and none understanding OBD1 and CATS TUNER to ask . Which also I think when I have and am using HP will help me be able to help those here with trans tuning questions and solutions better . My primary reason though for the swap is repeated issues with the optispark ever few months to a year since the factory one exploded at 220k miles and it seems all all the aftermarkets cheap or expensive seem to have about the same level of dependability and life span (not very long a few months to a year for me so far) and best I can tell even the reman GM are ifffy even though very high dollar and new GM simply no longer available.

Though all in all I think this area is the least worriesome for the OP as much as being annoyed / not used to the feel and action of a a performance trans with the Overun Mod which is not unique to my builds though my method is generally much simpler nor is mine the first as I have learned some other had played with it prior to myself 10 or so years ago and in fact SONNAX now offers a VALVE BODY with this function. Though there HD 2-3 valve did it prior but only in D3 . Though I think they came to the same conclusion I did that no one actually drive around in D3 or remembers to pull down when hitting it thus making its mostly pointless.
But the mod while making the sprag virtually indestructible (never seen a broken one with the FT OR MOD DONE TO DATE) Does indeed have the downside of a clunky 2-3 3-2 which is likely why even though you cans see in the VB design GM did consider it which is why it does easy to do. Is probably why they disable it in both D3 and D4 IT WAS NEVER ON IN D4 but was on in d3 3rd gear but off in D3 2ND gear and manual second gear . the annoyance factor varies from car to car with things affecting it from IDLE SPEED- REAR RATIO- ENGINE VACUUM PARTICULARLY WTH SPEED DENSITY and forced induction to settings for when the 3-2 happens and the 2-3 at near or zero throttle . In my own car the 3-2 happens real low at like 2 mph at 0 throttle so its light bump coming to a stop with 3.08 gears.
But I worked with guy who was geared 373 and super charged with speed density that dropped at 8 mph and between that and a massive pressure spike we saw during the downshift felt like someone hit him in the *** each time. We with great effort and time found the spike issues was the MAP sensor seeing Sudden Vac change during the downshift causing the trans pressure spike at the same moment .
He was able to solve it by doing something with the MAP table and lowering the low and 0 throttle 3-2 and raising the low 0 throttle 2-3 but sadly as with many questions here solved but the actual solution and method not shared I do not know what he did with the MAP to stop the spike.
Again sorry for the rant I always get carried away talking tech lol

 

You could certainly be correct, but I hate to dismiss the possibility that something is actually wrong as it might force the OP to live with a setup that's under-performing and might be more prone to failure.

To be clear, I'm not blaming your trans or trans modifications at all. I'm not really blaming the torque converter (FTI) itself either. I'm more likely thinking that something might not have gone correctly with the install (as it sounds like the shop botched some other aspects of this as well). Perhaps there was an issue with converter clearance that was either not corrected soon enough or not corrected properly. If clearance is a bit too loose, could it not lead to some of these issues (or cause an exaggeration of these issues)? As you mentioned earlier, most folks don't find your overrun mod to be so excessively harsh (especially how the OP described it initially being) and, based on my own experiences with this platform, I don't think that the idle behavior of that converter is completely normal. If clearance is a bit too much, it might not lead to immediate failure, but it certainly wouldn't be good to leave it that way. And I think an install error such as that could potentially lead to some (or maybe all) of the OP's concerns.

I guess I just have low confidence in the install shop based on what happened with the tail shaft seal and the fact that the OP seems to be having concerns that aren't (IMO) normal for the application. Sure, maybe he was, in fact, just expecting more of a "stock" feel, but it's also possible that the install wasn't done perfectly, leading to some exaggerated conditions.

 

I don't think converter to flex plate clearance being too little or too much would cause OPs issues. Too much clearance would cause the converter hub to pull out of the pump and strip the lugs from the pump gear. To little clearance could cause high wear on the engine thrust bearings and wear in the pump. If this where the case OP should have seen metal in the trans pan. I don't think install error is at play here.

Things to check though would be TSP, MAP and MAF sensors.

 

Damage could have also been done if the initial spacing was incorrect, and the shop found and "fixed" this before returning it to the OP. It (spacing) might be fine now, but an initial test operation might have hurt something if they got it wrong at first.

Still wondering what thoughts FTI has on that idle behavior. I suppose it could be "normal" for their converters, but it's certainly not normal for any of the several other brands I've ever used in this application.