To me, the only Epi LP which makes the cut is the LP Ultra, which is out of ur budget range. And can u plz state ur musical and tonal preferences, plus ur influences? That way, not only can we recommend u other guitars that might suit u better, we can also suggest some mods u can make to acheive that kinda sound. Unless, u've decided that u only want an LP. I think any of the lawsuit brands(Tokai, Edwards, Burny, Greco) wld suit u, they have several guitars in that range. Tokai at G77, Burny at Yamaha, Greco and Edwards at Davis. U might wanna check this LP out too, it's a virtually unknown brand, but ubermodded by Mike@SV. I was impressed with its driven tones, the installed pickups are waaaaay hot. The cleans weren't bad either, had a nice twangy sound. The body was pretty resonant(not sure of the wood, u can ask Mike), the setup was top class, no dry spaces on the fretboard, neck ramrod straight, very even frets. At this price, it's a steal. Here's the link:
www.standardvalue.com.sg, it's below the 'Sound Drive SG-100R in store!' YouTube video, jus scroll down and u'll see it.