I don't know if the 7.5 LSD's are easy to find or not. I know the 85 and earlier V8 Mustangs had them. If you find an 85 Mustang GT that is very near an ideal donor from that prespective. That is the last of the carburated Mustangs, and it had the 7.5 LSD, as did the 82-85 V8's I think. Earlier than 82 had a different style rearend that is basically junk.
Both Mustang axles (left to right) are the same length. Without measuring, I am about 90% sure the diff flange is centered on them. The axles are the same length and the cross pin is the center. The ring gear is to the side from that, and it seems to me the pinion centerline is centered with the crosspin. So the ring gear is offset, but the driveshaft is centered I am pretty sure.
I would be very surprised if you can't find a 7.5" rear that someone will give you locally. You should be able to get an old 8.8 fairly cheaply too....
In this picture you can see it is pretty much centered
The engine and trans in a mustang IS cenered in the chassis, and you can see the driveshaft goes straight back... so.... I would assume the flange is centered.