I was able to get vibration to work by installing the ForceFeedback Driver for XInput. It works, but it's a bit jarring and doesn't remind me of the satisfying rumble from my Gamecube days playing this game. I realized it's not that big of a deal as you can learn the edge of the strikezone based on the limits of the joystick. The rumble is almost bad to the point where I would prefer it off. But, I decided to leave it on for now as maybe better than nothing plus it can always still be disabled from the in game menu.
It seems like most old games work with X-Input, but the button mapping might be off. As long as the mapping is configurable and you have enough buttons on your controller for the game, then you should be good.
I got my Gamecube controllers hooked up using the Mayflash adapter, which is D-Input with vibration feedback. The only problem is it's impossible to configure MVP 2005 PC version with Gamecube controllers, because the Gamecube controller doesn't have enough buttons. The actual Gamecube version of the game works with additional button combinations, but the controller.cfg file only allows you to map single buttons to each command. (let me know if I'm wrong here)
I thought there was supposed to be a way to make a virtual controller with Joy2Key, so I could map Gamecube button combos to a keyboard command and make a control profile that way. If there was some way to do this I would attempt it. But I don't see that option on my Joy2key 5.2.1. Overall, though, I'm pleased with the X-Bbox 360 controller and Joy2key does allow me to navigate the menus from the controller.
I still have a few more things to test on the X-Box 360 controller like bunting, relay throws, fake throws., etc. But, it looks like the config I copied from this site is getting me all set to play this game, so I very much appreciate the guidance.