[Looking for an Epi LP with FAT neck! Is there any to find?]

You should have a look at the Epi LP Traditional Pro II. I just returned a Vintage Sunburst one a week ago because the NECK IS TOO FAT for my tastes.

The description of the guitar describes the neck as Slim Taper BUT IT IS NOT. It is a fat neck with a satin finish.

It is a great guitar and relatively inexpensive, ($500). It comes in several colors, and has coil-tap and DB Boost. Like I said, I sent it back because of the neck, but now I am considering buying it AGAIN. It was a really nice guitar, and I miss it already. Good luck.

[Looking for an Epi LP with FAT neck! Is there any to find?]

Take a look at the Traditional Pro II

This might be what you need. The neck is considerably fatter than the "normal" LPs (the Plustop, Standard, etc). It is inexpensive and has a ton of features, including some really cool color options. I bought one online and was shocked and surprised that the neck was SOOO fat compared to what I was used to. I almost returned it, but can't bear to. It is a great guitar at the price.