After many months of work, the Cruise for a Corpse engine plays the PC version of the game all the way through without any bugs.. I was also able to figure out and implement music and sound effects as well, although currently only the PC Adlib player is supported.
The Amiga and Atari ST versions of the game will probably play all the way through, although music and sound effects handling will need to be implemented for them.. I'll leave it up someone else more familiar with those systems to take care of that sometime in the future.
It's when you're diving into fixing and extending engine code like this, the old maxim 'The devil is in the details' comes to mind. Even the smallest mis-print or mistake in the code can cause errors that are hard to track down. It's actually kind of a relief that, as far as I know, it's all over and done with now.
Anyway, I plan to spend the rest of my vacation time (I'm on holiday until the 22nd) getting in some R&R, and some more generic mucking around on ScummVM - this will probably include some time spent working on the MADS disassembly, so people can look forward to further work on Rex Nebular in the near future. :)