Yes, I changed the design somewhat. Your advice had a lot to do with that. For now I'm going to stick with the L shaped bottom support, but I'll be testing everything for strength once I print it all out with the ABS. I may decide to add some to the inside of the corner on that L shaped piece though. It can't be much or it might get in the way of whatever can/cup is placed in the holder.
As far as the L shaped piece staying in place, it's such a tight fit that I had to tap it into the slot with a hammer. I didn't use any kind of glue, but there's no way I can get it back out.
Here is what the latest iteration of the bracket looks like (upside down, of course). It will be nice if this all works like I hope, and we have two very usable and accessible cupholders:
