Would it be difficult or impossible to put a carb into a 4.0?
Probably not very difficult, really. Just need an intake manifold set up to bolt a carburetor on top of it. I don't know enough about 4.0 history to know whether an early YJ or CJ manifold would bolt up to the head (my power steering pump I believe bolts to the manifold as well). If it didn't, you could probably have someone skilled at aluminum welding fabricate one for you. Then you'd need the mods to the fuel system to get fuel to it at the right pressure. and if you're converting and ditching the PCM altogether, you'd need a standalone ignition and new gauges, since the instrument panel is PCM-driven.
I don't know that much about the 32RH, but I thought the H stood for hydraulic, meaning it was not computer controlled except for the torque converter lockup.
If you did the toggle thing, you could keep your instrument panel but you'd need 2 fuel systems, and you'd have to get used to having a check engine light whenever you had that toggle switch in "carb mode", 'cause the PCM isn't going to like not having control over the fuel mixture. I'd put a shutoff valve in the carb fuel system, not just a pump that shuts off, or else you'd probably get codes for an evap leak. I also don't know what all it uses to determine spark advance and if it would do anything undesirable based on those inputs when it doesn't have control over the fuel. Going back into EFI mode after being in carb mode would probably take some relearning of the long term fuel trims and it'll run richer than crap, if not die entirely, until the bowl is empty.
Nothing seems too insurmountable if you really wanted to do it....no more complicated than a motor swap anyway.