"Popping the broken gear off of the motor was no problem, but getting a Slot.It pinion on the knurled shaft was an absolute bear!"
Yes, don't do that. Remove the rear axle assembly and get a small section of fine grit sandpaper. Add power to the car and hold the sandpaper against the motor shaft. Sand it until the knurling is flush.
Same thing with your axles. The aftermarket gears are made for a clean area.
"How could the axles be two different widths?"
It is rare, but sometimes you get an wrong size. Have a caliper? if so measure the diameter of them and you will see the difference.
"I noticed that the Slot.It spur is considerably wider than the plastic Fly one, the extra width being necessary to allow for the mounting screw"
Are you using a 18mm diameter 36 spur? (purple)? Even with the added hub for the screw, it should be pretty close to the same.
The Fly with hub is 3.75mm and the Slot.it 18mm/36 spur is 3.85mm
The teeth on the Fly should be twice as wide as the Slot.it.
I have the same car (LH) and make sure the gear hub (where set screw is) is facing toward the wheel and place the spur pretty much flush against the bushing.
"I figured that even if it wasn’t, the Slot.It pinion would carve the Fly spur to fit it."
You might not believe this, but it will be the other way around in MOST cases. If it had that grey colored gear then likely not. That polymer Fly used is useless and much too soft to work properly for extended periods of time.
On most other gears, the plastic will cut the brass pinion. I have seen many a pinion in the shape of an hourglass because of improper fitting (too close).
"Is there anything that I’ve spelled out above that I could have done better or differently?"
My best advice is to try not to mix and match. Remove the old stuff, and replace with new. You will find a world of difference and a much easier tuning experience. I realize that is not always the road we want to take, but just sharing my thoughts. I have spent many hours trying to do what you have done and it is easier to find out what women really want AND getting a winning PowerBall ticket on the same day. Once you get a few parts in stock, try it again.
Just trying to help.