M1 carbine receivers without barrels are (or are supposed to be) Restricted and therefore required to be registered. If an 18 3/4 to 20" barrel is put on, it can be de-registered. Once this is done, and you remove the NR barrel, and an 18" is put back on, it's now back to Restricted and has to be legally re-registered.
A barrel should clock up by hand with about 1/8 of a turn to go, where a robust receiver wrench has to be used to complete the installation. Threads are 3/4-20 TPI, so 1 rotation is 1/20 or 0.050". 1/8 of a turn is about .006", so if it clocks up by hand to 1/4 of turn, .006 has to turned off the barrel shoulder to get it down to 1/8 turn. If you or a machinist has never done this on a carbine barrel before, then don't attempt it (there's a learning curve). 52 degrees sounds about right for a hand fit up, if I read the OP's numbers right, so 1/8 turn is 365/8 = 45.6 degrees (pretty close to 52).
I've done a number of re-barrellings/chamber reamings, and bearhunter is right, they are finicky.