If it's a flat top les paul you want, solid maple wouldn't be quite so extreme as a carved top version. Also if you did want the tele bridge it'd be simple to fit.
With people talking of korina I think it's Hamer that make a korina les paul jr type guitar but I remember it being a special edition and £3000, having one custom made would be cheaper than that. Jonathan at Feline Guitars has just made a korina lp type guitar, he might be able to tell you more about how it sounds. It would certainly give your you're slightly brighter mahogany sound, a lp jr style body would help that too to a certain extent.
Also if your considering the custom route, maple tops while often used for aesthetic purposes brighten the sound of a thicker sounding body so perhaps combining a number of the suggestions in this thread may get you what you want, eg
Korina LP jr shaped body (chambered for weight?)
1/4 inch flat maple top, (at least this thick, 1/2 to 1 inch preferable)
maple neck
ebony or maple fingerboard
Heh have to stop, this could lead to some severe GAS :lol: