03 trans issues! Codes from dealer. Replace?

[Acdctennessee]

Hi guys, been lurking this forum for about 2 years now and it's awesome!
My trans recently started not wanting to engage from a dead stop, under light or heavy throttle. It is now to the point where it just shudders when you try to pull out. The fluid is definently burnt.
Truck is 03 with the 6.0 and 5r110, only mods are 4" turbo back exhaust with cat delete.
I scanned for codes with a edge insight as well as a el cheapo parts store scanner and came up with nothing. Had the truck to ford dealership yesterday and these are the codes they found. P0781, P0731 those are 1-2 improper shift codes? Also showing P0603 which is a PCM code I believe?
Dealer says the transmission is toast and wants to replace with
A reman to the tune of $4600.

What would the vets here do? With those codes do you guys think I'm definently looking at a failure? I'm a decent weekend mechanic, how difficult would it be to buy a reman unit and install myself? Are there any special tools I would need?

This site is killer and I have learned a ton here. Either way I go, I'll keep this thread updated!
Thanks forthe help!

[Acdctennessee]

Also wanted to mention, truck has 137000 mi. I've had it for about 2 and a half years and put 15k mi on it. Records show the dealership did a flush and filter about 20k ago