Paul,
I don't use LogMeIn, I used RDP (Remote Desktop) along with Remote Web Workplace. But, I still have LogMeIn there, because it's free.
Personally, I think (and this is just my thought), you are way overthinking this. I looked at Hamachi and wasn't all that enamored by it.
If you can answer one question, I will go away (although I have said that before, right). Why is there an issue with multiple users?
Can't your biller get to billing when she is in the office from PC A to Server?
Can't Nancy get to charts in the office from PC B to Server?
Can't you get to office manager stuff in the office from PC C to Server?
ALL AT THE SAME TIME?
If the answer is yes, and it would have to be, then why would LogMeIn be any different.
Biller LogsMeIn to PC A and then gets to Server
Nancy LogsMeIn to PC B and then gets to Server
Paul LogsMeIn to PC C and then gets to Server.
Try it, it should work. Then, tell me why you want VPN.