Had an older friend who allowed me to play with his collection. The MP40 can't be compared to other SMG's. It operates so smoothly that after running it and picking up one of a myriad others, there is just no contest! His was an early production and the workmanship was top shelf.
Bore butter is the bomb! Also, use my recipe for penetration, 50% K1 and 50% Majestic rear end dope (1:1) for a surprisingly affordable rust/seize breaker. Don't ask why it works, just does!
I would use MAP gas and bring it up to temp slowly and evenly. Should break loose-may have to give it a "tap". If you use any anti seize, make sure it is for high temp. Good luck! Don't worry about heating it up, it will take the heat. Just be smart enough to not smoke it.
I was fortunate to fire my friends WW2 example, and must say that it was the finest running sub I have ever had the pleasure to shoot. It was an early mfg date and the machine work was superb! Good luck on your quest.