I just found this article on the wiibrew site. It explains how to debug that ugly -but useful- crash messages the PPC CPU inside your Wii dumps when bgdi crashes.
I don't own a USB Gekko device (which is the preferred debugging method) but it should help during debugging nonetheless. Thanks, devkitpro guys!
So, if you find your Wii crashes when running BennuGD games, please send me a photo of the screen where I can read the text, and possibly the source code for your game and a little explanation or what your code was doing when it crashed.
This will help create more stable builds and might eventually help BennuGD upstream, too. So thanks for your help!