So Muhsin Mahdi's reconstructed Nights is a reconstruction of the Galland manuscript only, I find out, though the many reviews never seem to mention this, they all point to some reconstruction of an Ur-text.
The only addition he added from other sources is the end of Qamar Al Zaman.
The rest is him fixing up grammar or misspellings or what have you's. And his 3 volume set does a good job at comparing key textual differences. And of course he discovered the branching off of Egyptian and Syrian Ur-texts.