That's why I don't like Les Pauls very much and I've always been more of a super strat guy.
That's why I sold my first LP years ago. I just wanted to have more and easier accessible frets, a thinner neck and Floyd Rose action going on.
So after the LP I piled together: a Warlock, an Explorer (having all of the criteria above), a Jackson Dinky (also fitting all those criteria, but I was searching for something more stage-practically), 2 Dean ML's (sold one)... but most recently I wanted a) to get me a guitar with active pups again (none of the others have except the Warlock) and b) a real ballsy mahagony tone with a fixed bridge and the feeling of a Les Paul. So this came in pretty much perfectly.
Cool thing about that Epi is the 60s slimtapper neck. It's just SO MUCH easier to handle than the baseball bats you're usually finding on a Les Paul Custom.