I just put a rockauto tranny in a 2004 TB LT and I liked it. (About 1 year ago) It was ETE reman and if I remember correctly 100k warranty. You would have to get it installed by the correct shop for warranty.
I never had a problem with the stock tranny cooler but I did crack it trying to fix the quick disconnect about 3 weeks ago. (It started to leak(common issue), at this point I would have needed a cooler or new radiator (I guess they have rebuild kits but the oring is inside the connector), I was on the road, tried to fix it and screwed it up more. My radiator filled up with tranny fluid and I had to pay for a new radiator, a transmission flush, and coolant system flush. If I ever get a tranny put into a car again, I think I am going to get a NICE cooler installed. Something strong that will NEVER leak.
My car caught on fire when, after getting a new radiator put in, the quick disconnect exploded as Firestone forgot to put the quick disconnect retainer clip on. I was able to put out the fire with bottled water.
I now have hose clamps over the quick disconnect retainer clips. They will never come off again.
I do not know how much you know about tranny stuff, but all the stuff these guys are talking about putting in a transmission is not super simple stuff. I know you are going for a full rebuild, but if anyone thinks they can ever just drop the pan of a tranny and switch parts they are crazy.
I do not know what they are talking about strong transmissions also, I mean, after reading, reading, and reading, I found it was not even recommended to do a fluid swap on these things because of the over all design.
The 4L60-E is found in many different vehicle and people do all sorts of crazy stuff with it though. The ETE reman has a mild shift kit and I think some other stuff. I also looked into Jasper and Monster transmissions.
I went with rock auto because of the price and the fact that it was just a plain transmission. I just wanted the dam car to shift smooth.