Maybe a Lonestar 2x12 open back with a Mark IV head, 2x12 closed back cab in stereo with an A/B/Y pedal? Adding cleans behind a wicked gain amp will fatten up things, when blended well. Ask Steve Vai.
I have a 1998 SL-1 that was built at the factory right up until paint, then pulled off and sent to the Custom Shop, painted Black Cherry color, and final assembly. It now has the EMG "Lukather set" pickups with SPC control added to the control cavity. FU Upgrades Brass block, spring claw, and...
I keep some 1500 grit sandpaper on hand, and hit the back of the neck on my EVH B/W and worn 1973 LP necks to remove the skin cell buildup that occurs with an unfinished neck. Hit it with some lemon oil if you need to add back some of the slickness.
My junky looking 1973 Les Paul Deluxe(converted into a Standard) with routing and full size humbuckers. Lots of mods and upgrades to the things that make a difference. The neck is a 3-piece and sanded very well with 1500-grit. The profile is insane. As they say, "LIKE BUTTA". I have a 1998...
If it has the RP-11a preamp board, it sounds like one of the 2C>C+ upgrades that had the whole preamp board swapped. I would not sweat the power transformer.
I've had my 1973 goldtop since the mid-1980's and have tweaked it to my playing style. Other people playing that same guitar through my amp and cab WILL make it sound different. It is just the nature of the beast.