tl/dr - Perfect! Yes! The flywheel must have been installed backwards. You'd better take it off and check. While you are in there, have a look and see if there is a silly little crank spacer that was left in there before.
Before the ring gear is shrunk onto the flywheel, the flywheel is machined with a shoulder so that the ring gear has a shoulder to locate against; it is tricky to locate scalding hot parts that you are trying to shrink onto a large cold mass - best plan is to machine a shoulder onto the large cold mass; let the shoulder locate the scalding hot part! This is all an elaborate way of saying that the ring gear can only be in it's located position, unless some shady-tree machinist fucked things up, which is always a possibility with a 45 year old car and a 'rebuilt engine'...
The ring-gear mounting shoulder is cut into the flywheel in a lathe operation, as is the flywheel's mounting face area; the relative linear displacement between 1[the flywheel mating face] and 2[the ring gear shoulder/face] is a constant maintained for all L-series flywheels (ok, someone go find a case-breaking exception now!).
If your two starter motors each work acceptably with engine-1 but do not work acceptably with engine-2, then it stands to reason that there might be some mechanical anomaly with engine-2. (just so we are all on the same page)
The quickest check you can do at this point is take out the transmission, take off the pressure plate off, take off the flywheel, look at what the fuck is going on in there because something is screwy with either the flywheel or the mystery spacer. It is a Scooby-Doo mystery at this point. Blame Mr. Jenkins, the Amusement Park Manager!
[*]I recently acquired a 71 510
[*]I purchased it as a non runner <--- implying that the former owner was defeated by a mystery problem
[*]I'm not very familiar with Datsun
[*]I believe that the engine has been rebuilt <--- implying that the engine might contain problems. also, define 'rebuilt'
[*]It's too clean to have been run, the oil is new, etc. <--- implying that there is a major problem yet to be diagnosed
[*]It's a manual transmission <--- but the engine might not have been sourced from a vehicle with a manual transmission
[*]I tried to start it the other day
[*]It turns over by hand ok.
[*]the engine began to crank but the starter would not stay engaged in the ring gear
[*]the motor [turned] over for a few seconds, then... sounded like it was grinding against the ring gear
[*]the ring rear and the starter gear both [inspect as] ok
[*]the starter [was tested] off the car - the starter gear was fully advancing (extending)
[*]the starter from [a 72 510 with and auto trans that starts and runs fine] did the same thing when tried with the 'rebuilt engine'
[*]I'm hoping someone can direct me in the right direction as to why the starter is not engaging in the ring gear properly so that I can start the car and move forward with this project.
Other than that, I'm kind of stumped myself.
Also, +1 on what Robyn said.