I've got a couple videos of the printer running now, including the first print!
Here's a dry print from before the extruder was working.
And here's the first actual print, but with a not so great extruder:
And the result is, well, pretty bad!
But I think I can see what needs improvement other than just backlash.
The X and Z axis are very close to the expected 20mm, (20.78mm and 20.43mm respectively) so I'll ignore any issues in those axis' for the time being. The Y axis though is almost a full 2mm smaller than it should be, so I'll focus all of my backlash compensation efforts on bringing this value closer to 20mm.
The strangest part of the cube is the checkerboard pattern on the back of the X side. This could be somehow due to backlash, but it looks like it might be the X carriage rocking back and forth. It looks like the spring mechanism keeping pressure on the roller bearings lost it's integrity, and the bearings are no longer pressing against the rails. With no proper constraint anymore, every direction change angles the carriage in an odd direction. I'm redesigning the X carriage so that the top roller bearing can be tightened against the rail with bolts and I'm hoping that will fix it.
I'll cover how I'm dealing with backlash compensation in the next update.