Regardless of what fluid you put in there, a filter on the return line from the cooler might be a good idea, if not already there.
When the tranny failed, it might have put crud into the fluid, that is lodged in the cooler.
Adding a filter, like a magnefine, in the cooler return line will prevent any crud that is lodged in the cooler from getting back into the transmission.
A good filter is a good idea anyhow.
A brand new vehicle, the place to put the Magnefine is in the line flowing TO the cooler,
After a few thousand miles, the place to put the Magnefine is in the line flowing FROM the cooler.
I know that FORD has a TSB or so out about verification of flow through the cooler after a transmission fails.
They had issues with new units failing because the cooler was clogged with junk.....restricting fluid flow or even blocking it.
The best of transmissions will not be happy with little to no cooling.
As far as the fluid to use, use the fluid that is appropriate for the transmission.
The BEST fluid (if there is such a thing) is not good in the wrong application.
Look for the specification called for your particular transmission and make sure that the fluid that you use meets that specification requirements.
Also, just because a particular brand does not work in 1 application does not mean that it is not great in others.
I have never used Amsoil products, but have no reason to think that they are anything but top quality when in the correct application.
If you want to select a Amsoil product, go to the Amsoil website, select your particular vehicle and read up on what they recommend for your vehicle.
If you have any questions, we have several members of THIS forum that are dealers who will be more than happy to help you find the information you need.
Also, give them a look as a source for your Amsoil purchases.