Well, it looks like my issue is solved, but I can't explain how. I basically gave up getting MAME Wii to run since it wouldn't load games, and I couldn't find anything wrong with the file structure. And since no one chimed in on my post, I assumed that there was nothing obvious that I was doing wrong. So, I downloaded and installed Retroarch Wii and got that running with the FBAby bte4 - Homebrew Applications
In the HBC, I select MAME Wii v1.0 and it loads fine. I see a list of games, click on a game, but then after it loads the games, it immediately kicks me out to the HBC. The game never starts... I believe I have the correct version of the games 0.134u4 - but I'm not totally sure about that... Interestingly, If I try to load the HBB, I get an error that it can't find the homebrew list.by bte4 - Homebrew Applications