Strange. I have a CC in a Epi LP Standard and going in to my Marshall 2100 MkIII and Music Man 4x12 and the low end is there, plenty of it. I have the bass setting on the amp at 8 or 10 depending on what I'm playing.
Mine is a production floor CC, not a magnet swap from a ceramic Custom. I wonder if that has anything to do with it. It shouldn't since the windings of the CC and Custom are supposed to be the same with the magnet being the only difference but you never know.
The Custom may be better suited for you in this case.
Curious, have you inspected the body wood of your Epi LP Custom? If not, pop out the neck pickup and look at the wire channel going to the control cavity. You should be able to see some unfinished wood in there. My pickup cavities and control cavity are painted black. I verified mine is maghogany. The body wood will affect the bass response.