Well, I was/am not familiar with the CR-7, so I looked one up at FirstFlightBikes and get the jist. Yes, not much room to work with there. The ideas listed above/below are good ones, especially the Torx bit idear. It really depends on how comfortable you are in your mechanical abilities...there are a number of ways I would try...
You may want to try a small block of dry ice and while holding it with something that is not going to freeze your fingers off, hold it against the head of the screw for a bit to 'shrink' the screw. Not too long, because it will eventually tranfer the cold to the aluminum and shrink the threaded hole as well.
Buy a left-handed drill bit just smaller than the threaded portion of the screw. Should be somewhere near 1/8". Sometimes the friction required to drill, coupled with the soothingness of heat, will begin to back out the screw...or at least loosen it enough to get it started on the reverse.
Don't know how much room you do have, but have you tried getting a pair of ViseGrips onto the head of the screw?
I would assume that the screws used had some potion of LocTite on them, so you may want to try some solvent from the reverse side to loosen the LocTite.
When I posted about needing some mounting screws for a Judy XC brake arch, I had been in your position...the heads were stripped out and I virtually had ZERO options. I ended up buying a carbide, die grinder bit (the rounded cone shape) and ground the head off the screw until the brake arch was free to remove. I then used a pair of ViseGrips to easily remove the remaining screws. This stuff will make you grow old sometimes. I wish you good luck Shayne! Let us all know what ends up working for ya.