This is what LMI does, gives you an external URL to go to and see a list of your machines, isn't that solving the NAT problem? We have 10 PCs in the office and 3 providers who log in remotely with LMI.
Well if you had something like SBS 2011 Essentials or Standard, you get a nice little web portal called Remote Web Access which basically gives you a similar layout to LogMeIn where you can click which computer you want to remote into. Along with other things like files/emails. This comes out of the box with Essentials and Standard which is one of the many reasons you see SBS recommended so highly.
However, if you have a bunch of Windows 7 Pro's, you can still do it. Like you said you have one external IP but you also have 60,000 ports available on that IP. Most routers have the option of a public port (the one the Internet sees) and the private port (the one on your network/LAN). The private port will stay the same at 3389. You just change the external port e.g.
Dr. A has port 50,000 (Computer A=192.168.2.10)
Dr. B has port 50,001 (Computer B=192.168.2.11)
Dr. C has port 50,002 (Computer C=192.168.2.12)
etc.
It's a common security practice to avoid using standard ports such as 3389.
If you need some one-on-one assistance with the setup, just send me a PM.