I think it might only be the latter production of '90 BIIs that use MAF (11-'89 MFG date & later) if they had it at all.
My '90 is a 9-'89 truck and it's MAP.
Agreed on swapping the heads, however if there's another issue at work here such as your block being out of spec or you have cooling system issues, new heads are not likely to help.
If the '89 engine is much newer (less miles) I'd say go ahead and do it. Any sensors or other accessories that are different between them you should be able to swap over.
You might also consider swapping a 4.0L in too, as it'll bolt up just the same (though it's higher torque could threaten harm your transmission though, I suggest getting the trans that is mated to it at the same time and swap them in together if you go this route). The 4.0's extra torque will make it less fatiguing to drive, as it doesn't need to be wound out so much with every shift.