Have you checked here
http://www.lumenlab.com/forums/index.php?showforum=24 Plenty of 7"ers from I could tell.

You could try a google search of lumenlab and enter 7" builds also.
A simple rule of thumb, for mirrors in folded PJs same size as your LCD. Personally I try to use one the same size as my fresnel or one inch larger then my lcd. My reason is it is easier to only have to worry about exact direction then to worry about direction and placement.
Since it looks like you are ready to start planning and you are not sure of the overhead fresnel(s) you have. You are going to have to look at your fresnel more closely and confirm if they are fused together or not. find out what the focal lenth of the fresnels are and check to see if it is compatible with the triplet focal lenth you have before going any farther.
You may not need a collimator with that big hali work light but only testing will be able to confirm that. I assure you you will need some serious cooling with that light setup. and you are more than likely to have major hotspotting.
How come you don't want to use the rest of the overhead projector it has a lens and a descent lighting system.
I would recomend making a test setup board to get all the measurements and see if it will fit into the PC case.