Fiddled around and found one fix that works -- still requires two programs. Here it is: Import the ACAD .dfx (which was saved as version R12) into Corel Draw 11, then, with all objects selected, export using the "selected only" option as an ACAD version R11 .dxf file. I tried exporting from Corel using newer ACAD versions to see what happens, but nothing newer than ACAD R11 worked. R13, R14 and V2000 exports from Corel all hang the program on loading the file when the progress comment reads "Duplicate Entitiy Removal". The processor seems to be very busy doing something (don't know if the computer is hung or just doing infinite computations or something) and I don't have the patience to wait any longer than I already tried waiting, which was a couple of minutes at the longest. The R11 Corel copy loads immediately.
I can get out of that hung state by closing LCAM and Windows claims that the "program has stopped responding", but of course Windows does that a lot when a program is just really busy and not crashed.
Perhaps my biggest problem here is that I am using AutoCad 2005. It only saves .dxf files back to version R12 format, but then again, in other places in this forum I hear of people saving as R12 and having it work. And could that be some difference between ACAD 2005 and whatever version they are using? Ah, technology!
One problem remains: Points were converted into small circles when importing into Corel, but since they are just points where a drilling operation is going to happen I can tolerate editing the G-Code (as long as there aren't too many. Still need a better fix!
Okay, so I didn't give up!

I'm still hoping for a more direct way to get from ACAD2005 to LCAM so if you have a technique I would love to hear it!