YouTube has a bunch of videos showing how to DYI a screen or screen/digitizer repair:
https://www.youtube.com/results?search_query=droid+maxx+screen+replacement
I've never done it myself, but that may be the right place to start.
I use a Griffin clear case for my Maxx. It's pretty minimal, has a lip that hangs over the bezel, so I think it will give me at least a little protection if I dropped the phone. If you can't afford to repair or replace your phone, or pay for insurance, paying a little bit of size I think is worth it if it will at least help protect the phone.
The edge to edge glass I think is the major problem. It can be the toughest gorilla glass, but it's still glass, fragile, and subject to fracture. It's probably unlikely that phone manufacturers will switch to larger bezels at this point, though. So, I keep my phone in as minimal a case as I can, with a Zagg or tempered glass style screen protector (unfortunately, there are no tempered glass protectors for the Maxx/Ultra), and hope that gives my phone a little more protection.