You should've known I was going to come in here and make a comment supporting PRS. The typical PRS is NOTHING like a LP. If you can find someone locally or a shop around town to let you play a short scale PRS IE: Santana, Ted McCarty SC or DC or a SC245, you might be pleasantly surprised. All three are available with big necks, all three sound huge and the shorter scale gives them the "Les Paul" -esque sound and feel. The biggest things you're going to have to overcome sound and feel wise are 1. the short scale/pickup spacing and 2. the body to neck angle. Very few, if any, other manufacturers build with as aggressive of a body to neck angle as Gibson does on the LP. I know that sounds like mojo talk, but it creates a specific feel. Super strats ala Suhr and TA have little to no angle what so ever which feels very different. The short scale on a LP gives you the ballsy neck tones too. The neck pickup is actually closer to the bridge pickup in relation to most other guitars.
My support for the three models I mentioned.
1. Similar set neck construction. The heels will feel familiar to you.
2. The short scale PRS (24.5") lean towards the Gibson feel (24.75)
3. The pickup positioning in relation to the shorter scales is much similar.
4. The average PRS is usually 7lbs or so give or take. The singlecuts will be a bit heavier than the DC models, but still substantially less than the typical LPC.
I wish you were local, I'd let you hold on to one of mine for a few days. My old PRS (96 Model Custom 22) really feels LPish to me, hence why I ended up flipping my 04 Standard a little while ago.
On another note, I was highly impressed by EBMM's Axis Super Sport the other day. Bolt-on neck, factory loaded Dimarzios, light as a feather and ballsy as all get out. Very mid-heavy tonality with sharp attack and a very signature "grind" to the mids. Might be worth a spin. Worth noting, the necks are narrow, but feel fan-fucking-tastic.