Let me take a look at the spur and see if it is in fact on backwards (wouldn't that be embarrasing .

It's not the driveshaft, as I assembled it once without the driveshafts even attached (to check for that issue) and the binding still occured. I'll check the spur gear orientation and report back!

Thanks for all the replies.
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Update

Yes - it was in fact the spur gear on backwards. Very frustrating as the recessions for the screws are actually more pronounced on the wrong side of the gear (which is how I made the mistake thinking surely the side with the proper screw recessions would be the side for the screws!)

But it all fits great now, with no binding and very smooth.

Thank you all for the help - I've been trying to figure this out for hours and never even considered the backwards gear. Now to solder up the electronics and go race!