You can still get a MG. Just get your C&R license first and shop around for a nice C&R subgun. Any "original" WWII MG should be C&R eligible. While Thompsons and MP 40's are prohibitively expensive, the .45 ACP Reisling SMG is still under $6K or so.
There are also newer MG's that are on the C&R list. For example, orignal Armalite AR-18 assault rifles are C&R eligible. I'm not sure on the prices on those right now though.
Be aware that you still are restricted to MG's registered in the NFA database before May of 1986. That means even if you found a 60 year old Thompson SMG in an attic somewhere, unless it was registered in the NFA database as a "transferable" MG prior to May of 1986, there is no legal way for you to own it. That's why a lot of old "war trophies" are getting destroyed as the vet's who brought them home die and the families find the guns.
You basically need to make sure the gun is both "transferable" and is listed as being C&R eligible. You need to watch out for guns that you think are C&R guns, but that were actually built up on new receivers. These are commonly called "tube guns." A "Tube gun" STEN or MP 40, for example, would not be C&R eligible.