I’d play around with your amp settings, and try playing with the knobs on your guitar.
When i play with heavy distortion, and i want to back off and give my guitar a cleaner sound, i just roll off the volume of my guitar knob. Think of it as using your knob as a boost, keep it around 4-5 or 5-6 for verses, choruses, parts that may require a cleaner sound and when you come to a solo, turn it up to 8-10. You can see me do this with my guitars in my videos (and ill probably do a lesson on this in the future).
Also, if you’re not comfortable rolling your volume up or down, set maybe your bridge pickup to the full on volume at 10 and your neck pickup at 5, that way you can go from clean to dirty with a flip of your selector switch!
I will say though, the pickups in the epiphone les paul customs are notorious for sounding muddy, the one i have is the same way! You just got to experiment with what works for you man