aamco did a trans for me many years back in my S10. They were fine. Its just another day for them, just another trans. I would, however, stick with a smaller shop and do some research for the "good guy" in town... There is always the "go to" shop in any town. Fred's transmission, local chain to me, did a great job for me on two trans' last year. A 700R4 and TH400 for my street and plow truck... Good guys, and each chain store acts as their own small shop... So its not like a subway ya know...
I would agree with the flush first/repair or delete the cooler.
-JD