New Clutch Question

You said it, still works fine. You didn't kill it, you just put like 10,000 miles on it in one dump of the clutch!
NV5600 clutches are pretty good. Seen guys run added power through them for a lot of miles.
But if you need a clutch.......Southbend.

In the old days I drove cars with failing clutches for 10's of thousand's of miles. Granted, that was a Toyota Corolla and you're talking about towing so it's a bit difference. I'd at least run with it for a while and see how it feels. You usually have a lot of life left even once it starts to slip.

No, I would not replace the clutch for one burn-in as long as it holds now. May still be good for 50,000+ miles.
If you need to spend some money consider some 4.10 differential gears to make it even easier on the clutch.

Typically, a clutch will start to slip long before it's ready to totally let go. If you notice your engine revving sooner/higher than before, or you've fully let go of the clutch and notice some play between engine and speed, then it's time to think about getting a new clutch.

If it works and feels normal, why replace it? I would not, however I have never got a clutch that hot.