lr-mupen64plus-next is released. And it is good, you must try it and ignore my previous post. It is in the experimental section.

So I ended up doing the following:

I left the basic config in place.

I then tested each game, changing the controller type to analog once the game was started and if it worked, I created a custom config for that game that has the player 1 and player 2 controller set to analog.

So now each game works as it should, some work fine with the default settings and the d-pad only, others work with the analog stick. I couldn't find one blanket setting that worked for all games, I had to test each one and configure different options files for each game that supports the analog controller type. It took a good amount of time, but works like a charm now no matter what game my kid fires up on the unit.