About the only firearms you list that you can TOUCH in your price range may be the MACs. LEGAL, TRANSFERABLE full autos are very pricey. My personal preference is the Uzi, but there is no accounting for tastes. If you can go shoot several, try that, and see what you like.
You do not "get" a class III license- you have ownership of a full auto transferred to you by a dealer that has a Class III endorse met to his license.
The only effect a C&R has, is that there are certain C&R machineguns that can be transferred directly to you- but you still have to do the whole National Firearms Act thing- prints, CLEO, $200 tax stamp, yada yada.
Have it transferred to a properly structured trust will bypass the CLEO approval and prints. Use a real lawyer for the trust, not a computer program.
Only full auto .22LR I have seen that impressed me was the American 180. Designed for .22 LR from the ground up. The firearm is the serially numbered parts (except for a few that have a registered SEAR.
Not to give you an abrupt answer, but sounds like you have a good Class III dealer- go talk with him, let him educate you. When you see prices, and the cost to feed one of those hungry critters, you may reconsider.
I do sympathize with you- I want an M60.