Good luck on the search.
FWIW, there was a big change in Les Pauls shortly after 2005, when they split the line into "Standard" and "Modern" designs with locking jacks, extensive chambering, etc. For better or for worse, non-custom shop LPs were measurably more different than the classic recipe after that date. For those last few years, you could also have two different necks - 60's 'slim taper' or the chunkier '50's' version. You may want to extend your range just a touch.