Recommended Tranny upgrades

[ChrisCNC]

2003 F250 SD with the standard upgrades (4" exhaust, Stage II intake, PHP tunes). I'm awaiting 80HP LT tune and will be towing our relatively light 4500lb trailer, 2 kids, gear and a dog around the mountains of Oregon, Washington, California and Idaho. I've got 35" tires.

I've done nothing to the transmission yet, but can feel quite a shudder when taking off from a stop, and it is worse when towing the trailer. I assume it is the transmission slipping and would like to upgrade before I find out I should upgraded and am stranded alongside the road with my family. While I'm waiting for my custom tunes, I've been using the tow safe tune that comes stock on the edge evolution programmer. Using stock tires my tranny temps maxed out at 220 degrees while going to the top of a 4000' pass over 10 miles (max less than 10% grade).

What all should I be considering? From my perusing the forums, I see that an upgraded tranny cooler (truCool or 6.0L ford cooler), BTS Valve body, and aftermarket Torque Converter are all good ideas.

What Torque Converters are 'good' ATS has a whale of a warranty on some of theirs (5 year, 500,000 miles), I've heard good things from Banks. I'd like to hear from one of the PHP crew on this one (Bill, Cody..."if it were me, I'd buy a ______") or anyone else that has an expert opinion.

What would be a laundry list of items I should prepare for?
Torque Converter upgrade
Valve Body upgrade
Tranny Cooler upgrade
???
???
???

I do rod around on occasion, but am more concerned about towing and tranny longevity.

Thank you,

Kevin