I was in a similar situation about 8 years ago, I went into a guitar shop with every intention of buying a Gibson Les Paul, I played a few top epiphone ultras, the gibson, then a top of the range Tokai, the Tokai blew every guitar in the shop out of the water. However as much as I loved the guitar it did bother me that it didn’t say Gibson on the neck. I sold it 2 years later and will always regret it.
If I were to have the budget you have, I’d go custom shop fender or PRS, something in tiger eye or elephant grey. You will want the name for that kind of money but IMHO a Gibson won’t have the quality or even be close. I’d spend 1500-2000 on the guitar and 1500 on a kick ass valve amp.