Me too, puppet nerd, definitely not IT nerd! Hope you find a way out of this, but I don't have any suggestions other than investing in 5 iMacs, and I suspect your budget is pretty well spent.
Try contacting the guys who put out dragon, I had an issue setting up dragon with my old canon 40D and they were great with walking me through the issues. I'm certain they could help you with a connection issue for sure
Which version of Dragonframe are you using? If it's older than 3.5, the 700d won't work according to the Dragonframe site: http://www.dragonframe.com/cameras/canon_eos_700d.html
There's more info about the camera and DF in that link, and some specific instructions for Windows.
I was just on the Dragonframe site, says that EOS 700D camera is not compatible with 3.0 version of the software. Try updating to 3.5.
That still leaves all the PCs with Stop Motion Pro not working with the 700d, but if a later DF will work, that's gotta be cheaper than replacing the cameras.