Not sure if it's the same on all cars, but on this one the tab that sticks down for the lower clamp on the outside is longer than the one on the inside. Either that caused the instability or a spot weld was thicker in one spot causing it to not seat properly.

I also noticed that the top bracket had a notch machined out of it, but there was nothing on the rail that would interfere there.

Also 1 quart of fluid seemed way too much. I got about maybe half to 2/3rds of a quart, though I didn't have much leak out when I pulled the heat exchanger.

Also of interest, this cooler is much taller than the fill plug on the transmission. I'm guessing this may complicate things.

I injected around half a quart of oil into the trans cooler once it was in place before it started spilling out. Then I went to fill via the trans drain plug and it started pouring out quite rapidly.

Once I'm ready to start the car again, I plan on lowering the trans cooler and letting it warm up and circulate fluid. I'll then do the standard fill procedure via the fill plug so that it's just slowly dripping out. Thoughts on this?

Yes, the tab where it sticks down is where we clamp to. That's the normal location.

The top notch should be where the frame has a weld seam.

Adding fluid will depend on how much was leaked etc, our 1qt is just an estimate and a minimum amount for purchase lol. Fill plug being under the cooler has nothing to do with it, it's a full pressurized system. You should just fill fluid just like the manual states.

So you're saying gravity will not cause the fluid from the cooler to drain down into the trans/pan? Seems a bit counter intuitive unless I'm missing something.

When the car is not running it will. You need to fill the transmission when the car is on.

While the car is on and running on the lift, you will put the car in different gears.
Add oil to the trans as needed until you see it leaking. That's when it's full.

What is the minimum trans fluid temperature that we would want before wide open throttle or racing situations?
I installed the BMS trans cooler kit this past May. The kit is awesome and it definitely worked great this summer. Here in the south east I hardly saw 160 degree trans temps during mid 80's and 90 + degree weather.

Now that Fall has begun I took the car out the other evening with ambient temps around 55 degrees. It took almost 30-40 minutes just to get the trans fluid to 120 degrees. Is 120 degree trans fluid enough to enjoy the car or will I need to block vents / install thermostat for colder months? Besides the cooler temps my transmission has been super happy since installing this kit on a MMP s3 / full e85 / PI e92.

120* is fine to start playing with it.