Finally, after two months and three attempts, I am back where I started, with an M&L 3DS XL with a fresh screen! It's probably for the best that I got a refurbished unit; my original one seemed to be working perfectly, but I did have a little trouble that one day after I was carrying it in my backpack during a colossal rainstorm.
I borrowed a 3DS from someone who apparently did not mind losing his save data; I did a System Transfer before sending my old unit in, and just now did a System Transfer back.
At least I ended up with an extra power supply, stylus, manual, AR Card set, and 4 GB SD card.