Unfortunately, your picture is blocked through the proxy server at my work, but I'll check it out later this evening.
I'm a little confused by the use of the term "gaps," since the rear cross member welds directly to the rear frame rails, effectively closing the loop on the rear frame itself. The lower taillight panel welds to the rear cross member itself, and there are a pair of brackets that also butt up against the inside of the taillight panel for the rear bumper brackets to bolt into - not much in the way of "gaps" to contend with with these pieces. By not removing the quarters until the taillight panel, trunk pan, and rear cross member are replaced, the taillight panel should line right back up and fit into the area the original piece came from. Granted, mine was straight - albeit as rusty as the Titanic - but if the repair shop got the back end anywhere close to straight [despite the bent rear cross member] it should all fit right back in fairly well.
If your rear cross member has been compromised, rather than try to straighten it out (and possibly weaken it further) you might consider just getting a new one and replace it altogether.
https://www.npdlink.com/store/products/mustang_rear_floor_crossmember_repro_exact_fit-146898-484.html
If the rear frame rails themselves are also bent, there are replacements for those as well (which will become a much more involved repair, of course). If you choose to straighten out the ends of those instead, the rear cross member will help in establishing the side-to-side distance... obviously you'll want to center it on the vehicle as well to get it 'back to straight' if it's also tweaked one way or the other.
Hopefully, it was just superficial damage to the taillight panel and rear cross member, and the previous repair shop just tacked on a new taillight panel, bumper, valance, etc., thinking that nobody would really care about the rear cross member once the 'pretty stuff' was all back in-place. You might actually get away with just replacing the rear cross member (along with the rest of the sheet metal items you already planned on doing).
I hope I didn't go off on a completely different tangent, since I'm not able to see the pic at this time. I wouldn't want to give anyone the impression that I take this stuff lightly and am just hoping you get lucky with this repair or anything.