A 700r4 is not all that horrid behind a 6.2 since a 6.2 barely has enough power to pull a greasy string out of a goats ass. Well in comparison to a Cummins or Powerstroke anyway. The main difference is the Torque Converter and the Governor. Any governor can be converted by changing the springs. Probably easier just to keep the current governor that's in your now. It wil interchange to the later model core as bucket said. 87 at minumum, but 88 and up is preferred. If you find an 87 that's a good deal, don't hesitate but the 88 does have some changes the 87 didn't have.
So find a later model core 87(88)-93. Use your current governor and replace Torque Converter with one stated to be for Diesel engines. Plan at bare minimum, Beast or Smart Sunshell, Commercial Alto or equal 3/4 Clutch pack, not the Z pack that some think is better. Vette Servo, Wider 2/4 Band, and Trans Go Jr. shift improvement kit. Seems I'm forgetting at least 1 other item as the bare minimum.
Not going to be turning higher rpm, so no need to sleeve the input drum as I usually recommend and that's not in the bare minumum anyway, that's more needed for higher rpm or moderate to heavy off-road use.
If it comes to me, I'll update with another post.
Here is what the Commercial Alto 3/4 Clutch Pack contains. You can usually match it up with other brands and make the same kit yourself by just getting these parts.
This kit contains 9 .062" 3-4 friction plates, 8 .060" 3-4 steel plates,
2 .076" steel plates, 1 .125" top pressure plate,
and a .062" top snap ring.
Comes with instructions.
No special transmission tools required.