Manual to auto swap

You would most likely be cruising at under the stock convertor's stall too. And here's why;
Let's say you had a 2200TC, and your car was geared to turn 2200rpm at your cruise speed.So you motor up to that cruise speed, and back off the throttle.Until the speed is stabilized, you will back off , back off and back off until the power output of the engine matches the cruise requirement. Now look at your tach. It will not be 2200. unless your engine only puts out that cruise requirement, like 30 or 40 hp. More than likely your cruise rpm will be under 2000, or even less. That means the TC is slipping at least 10% or more. And they go 200,000 miles or more, that way.
Now getting back to your question; No, the TC will not burn up, nor any other part of the transmission, from being operated this way.
Of more importance is the fact that the 4x4 truck tranny will not fit into your car. To make it fit will require the complete tear down of the tranny to swap out mainshafts and then a car extension, and probably a car governor as well.
And there's nothing wrong with running a loc-up in a mild combo.

I hope by now you have figured out that the crank issue is a one way street,mostly. After 1966,you need the right crank to make a bolt-in swap to a 4-speed into where an automatic once was. The 4 speed can be made to fit any 66up crank; it just might not always be a bolt-in.
But any 66 up LA crank will accept any 66 up 904/727 based TC/trans.
So for you, it's a non-issue; with the 71 or later 360 and the 80's tranny.

Now, one more thing; Why do you think you need a 2500TC?
What's your combo? What gears,rear end,car weight or body,tire size,cam, and intended useage?
The stock truck TC might just be fine, depending on the answers to these questions.

I guess you also know that most A-bodies require: a specific engine-type K-member, and engine brackets, and motor mounts, and often a throttle cable, and car specific KD linkage, and a car filler tube, and car manifolds ? And 9 inch brakes, if you got 'em will have to go, and I would not run that old style M/C either.You are just asking for trouble, and then all your work,time,and money, could be lost in an instant, not to mention people's futures or lives.