Sorry for your lack of satisfaction......
But it kinda sounds like you're describing a pretty good selmer style
guitar .
The real selmer style sound really is a thinner sound ....they have only mids and highs....not much low end at all.That is common with all the good ones I've played..Busato , duponts , gallatos.
The mahogany you described is because it is laminated back and sides like the originals...the other gitanes are solid not laminated .
I think the tailpiece is the same as on the other gitanes with the exception of the insert and the frets always seem to need to be dressed....you may want to give it a couple of more days trial period , and make sure you have the strings swapped to argentines or equivelent gypsy jazz strings.
I have been more than pleased with mine and would stack it up against almost any I've heard or played....they just need to be set up first.I even kept the original bridge on mine ...which many opt to replace.
I too tend to like a little fuller sound...and thats why my other guitar is a Dell Arte Hommage (Favino style) which is absolutely superb.
But for the selmer sound , the JJ is as close as I'll probably ever come.
good luck.
David