It’s good to have the special 1/2” socket tor rotating the engine, you could then feel if the engine is unusually tight or has some resistance besides the compression bumps.
If it ran for 10 minutes and didn’t die on its own but you shut it off, then I’d agree with you that the fuel system is at least functional.
If you put your good , fully charged jumper pack directly on the starter and it cranks in a weak way and too slowly to start, then there is a very good chance that the starter is the problem in spite of the fact that it was rebuilt with new internals. We are talking here about electricity and humans, these are often the source of errors. All’s it takes is one bad connection or dirty solder joint on your starter’s 4 brush leads or other internal connections (that were just redone) and it’s going to be weak and under powered. You have to somehow verify that your starter is in fact as good as you think it is.
Can you get the rebuilder to test it or buy a cheap one online that can be returned, these will work well enough to do a test and compare to your rebuilt one.