Offset fill leaves white spots in the center

That suppresses the symptoms by having the laser head move in the same direction across all the scan lines.

Diode lasers generally move slowly enough that the laser doesn’t lag behind the motion. The offset in your pictures looks to be on the order of a millimeter, which is much more than any possible delay due to the electronics.

“Fixing” backlash with a timing offset hides it by adjusting the timing to match the backlash. If you measure the offset at a wide range of speeds and find they’re all pretty much the same, that’s the amount of backlash.

Yes.

Not to sound dismissive, but that assumption is totally wrong.

For example: