I don't know a whole lot about the push button part of that system (controls, actuators, if a computer is involved?) but I suspect the control mechanism is similar to the heavier duty units out there.
It's not particularly the transfer case I'm worried about, so much as the transmission, and your T case is unlikely to "bolt up" to a stronger trans as there will likely be a different spline trans output.
Yes, you could likely swap the input on the T case, but it would likely be easier to buy / trade for a trans & T case combo that already bolts together.
If you prefer a manual trans you might be able to get the apropriate combo out of a similar year Chevy / GMC pickup (heavy half ton, std 3/4 ton, especially anything with a tow package).
At least the connections should be similar for T case and speedometer.
Kinda surprised the 4.3 is giving you grief, but after this much time (17 years) everything can wear out.
Not to discourage you from diesel, but a smaller V8 Chevy (ie 305) would likely be a simpler swap, and will have more aftermarket support.
Had to say that, wouldn't be fair if I didn't at least mention it once (then you could even buy a wrecked similar year or newer truck for the
engine, trans and T case, and as I'm sure you know they are quite a bit more common).
If you are intent on diesel and need one sooner than you can find a 4BT, might I suggest either the 4BD*T Isuzu or the OM series of Mercedes diesels.
As I understand it adapters are available for both, while I personally wouldn't want to put a 4BD in front of your trans or T case, I wouldn't have the same concern with the Merc, as I understand it they are physically smaller, lighter and smoother running than either the Cummins or the Isuzu.
Food for thought, best of luck.