If the GWX install on D:\ works fine, WITHOUT having to have the disk inserted to play it, then what you outlined should then work fine.
I assumed (correctly, it seems... odds were in favor of this being the case..) that you would likely have a 2 hard disk set up in your computer.. as most do.. even including Myself...
I was figuring on your having the clean install set aside on the 2nd hard drive & was attempting to run a copy (or in this case copies) on the main or C: drive.. & the way I outlined, would also work.. as I have 2 copies of it set up that same way. LSH3, being 1 of them..
The main difference being, My copy I have (clean unmodded backup that it is..) was bought & paid for, through Steam, but.. divorced from Steam, using a program to do this, created by a former subsimmer, no longer around on subsim, though...
Sooo... the way you have it outlined, I'm fairly confident, would work.. since having them on 2 separate drives. I assume, hopefully correctly, the back up is on what.. an external drive, perhaps...
M. M.
p.s.
Just make sure to run multish3 with the new fresh install for running LSH3, so as to ensure the save game folder is separate from the GWX one.. of course..