Hello forum
Just doing some general research right now and I figured I'd post some questions here. Sorry if this is considered low quality, its not my intention to crap up the board with pointless/repeated questions but I have a lot.

If you want to ignore the context of my rambling: Does the 05-08 GS300 RWD with a 3GR-FSE have an A760E or an A960E transmission? Will an A760E work with the 2IS250 4GR AUTO ECU? What would be the results of that swap? Is it possible to source a 3GR-FSE with an A960E attached to it? Has anyone swapped it out for a better standalone (ive seen one swap online but I'm not sure what was going on with it)?

If you care to understand why I asked the question:

I've tried searching for the answers before posting here and I figured I'd try and ask Lexus ppl to get some clarity. I own an 09' Lexus IS250 RWD with 155k on the dash, its my daily. California owned for most of its life, lives in the south only up north for a couple winters and it hardly saw snow with me except for this past winter. Its very clean underneath, bought it at around 120k. Sadly, I cooked my transmission and It needs rebuild/replaced (I'm embarrassed to explain how). I planned on going to a junkyard and trying to find a lower mileage wrecked rwd 06 GS300 as Ive read online that they can have the A960E or the A760E and I guess my question is, would I be able to find a GS300 with an A960E already attached to the 3GR-FSE? Or even better would the A760E be plug and play as well just like the 3GR or would that be an issue? Would there even be a benefit to swapping for an A760E. Would the ECU throw a fit because the sensors and pressure regulation is different or different shutoff valves/etc.? I'm not familiar with transmission nomenclature so sorry if that one was vague.

I can source these drivetrain components from different vehicles if I need to but I figured it would be cheaper and easier to source what I need from one. A motor upgrade and a replacement transmission is still going to beat the price of a rebuild, and potentially the quality of one too. Ive called 10 rebuild shops and only 1 was willing to take it. If they aren't confident, I'm not either.

I figured I'd just replace it because I don't want to drop 3k minimum for some rebuilder when swapping it would just be cheaper. And I guess while I'm doing that I might as well swap the motor because while the 4GR is fine, but 3GR makes more power out of the box, lower compression ratio, and it's supposedly a direct bolt no tune needed (but recommended). I already wanted to do it if I got the chance but I think my chance to do so is here.

Also anyone reading this, have you done the swap yourself? I read you need to swap the intake from the 4GR to the 3GR but thats it. Is it quite literally just unplug everything -> place the new power plant -> hook it back up -> vehicle starts (aside from normal swap issues). 0 wiring needed, no tuning needed, just plug and play.

Unrelated question, why does the 4GR give off so much white smoke? I swear I have checked coolant so many times and its not losing any, oil always looks fine during the change. its not billowing but its very noticeable, even when its warm and the cars warmed up theres a slight amount.