I just wanted to mention that I, personally, have no issue with going iOS7-only.
However, I think MrC made the best suggestion. The issue is that I agree with some other users here. JRemote is a good use for older devices that don't have the oomph to run modern stuff, but which still otherwise function perfectly. Throw it on the living room coffee table, with JRemote and a few other remote control apps, and it could be a perfectly functional remote, even though it doesn't have the newest hotness. I don't happen to have any of those devices, but if I did, that'd be exactly what I was thinking about doing with them.
And, as he mentioned, I'm happy to pay for an upgrade. I use JRemote probably second only to my podcasting client, and it'd certainly be worth throwing a few more bucks your way. I also think the massive changes with iOS 7 are a unique opportunity to do this with less screaming from the bleachers (some people will, of course, scream about the "paid upgrade", but fewer of them will, because it will be somewhat "understandable").
Fork the code. Keep the current version in the App Store, clearly marked as the "old version" for backwards compatiblity, and release JRemote 2 for iOS7. You'll get some screams from people who are angry that they have to pay again, and a few more from new people who accidentally got the wrong version (maybe lower the price of the original one since it won't be developed much anymore), but you'll get "upgrade revenue" from people like me, so I think that'll soften the blow a bit. And, most importantly, you won't have to kludge it with two nearly completely independent UIs internally.
If you're ever going to do it, now is the time.