One of the guys in the club has a Hepburn that he is willing to sell and I'd like to get it because the price is right and it's in better than average condition cosmetically but the bore is terrible. The only cartridge designation is a 38 stamped on the bottom barrel flat just ahead of the forearm which I assume to be either 38/40 or 38/50 Remington. If I get it I can either line the barrel and keep it in the original chambering or re-bore and chamber it for an easier cartridge like 40/65. How much of a problem is it to load for the Remington cartridges and is it worth it?

"38" on the bottom of the barrel could be more than those two cartridges. Could also be a .38 Long, or a .38-40 Win. or .38-40 Rem. so no guarantees until check it. But since you're going to reline it the cartridge doesn't really matter.
Average condition with a bad bore would still bring probably $1200-$1300. Once relined it will be worth more than you'd have in it then. Without seeing it I couldn't say more, as condition, and features might add some value too.

38-40 Remington is also made from 30-40 Krag or 303 Brit. Seems like the biggest problem for everyone is obtaining dies. Multiple guys in the forum, including myself, could help you with the brass until CH4D gets around to making dies. Lovely cartridge to shoot in my opinion.

Logan