Hi,
The problem with synchronization is that the mechanical synchronizers of the era synchronized the release of the firing pin and no the transit of the bullet through the propeller rotation plane. As there were several sources of random variation, the most important probably being the delay between the firing pin strike and the ignition of the main propellant charge, and one systematic variation unaccounted for by the synchronizer - engine speed -, the projectile transition point could actually be anywhere on an arc section.
If you've seen sychronizer test targets that were mounted on the propeller, this arc section is actually visible on them as a series of bullet holes. I think there are photographs showing Anthony Fokker with such test targets, and they were used in the same way by the Luftwaffe in WW2. The term for this test was "Auswanderungsschießen" ... "creep firing (test)" - because the bullet holes crept along arc when rpm was changed.
The available arc section and thus the allowable rpm range and mechanism/ammunition tolerance range was much smaller with a contra-rotating propeller because the second set of blades intruded into the "clear" area from the opposite direction.
If you're faimiliar with the Heinkel He 119 ... Heinkel actually projected a successor with the same layout, including a contra-rotating propeller, as a reconnaissance aircraft. When the Luftwaffe asked for a night-fighter instead, Heinkel switched the He 219 over to the conventional twin-engine layout since synchronization would have been really awkward with the contra-prop - and German synchronization system used electric priming, which generally was much more practical than the mechanical systems used by the US.
Here's a picture of the synchronizer used on the XP-75 ... the document it's in has some more (mostly non-technical) information on the history of the XP-75:
[URL unfurl="true"]https://ohiomemory.org/digital/collection/p16007coll92/id/559[/URL]
Regards,
Henning (HoHun)