Can't promise that a 'bent would eliminate your pain -- you'd have to try it and find out. But a lot of people, some with medical conditions that gave them serious pain on upright bikes, find recumbents painless.
My own experience: I don't consider upright bikes "torture devices" as some recumbent enthusiasts like to call 'em. In fact, give me any sort of bike and a week or two off work, and I will have a great time touring. But at the end of a long day on an upright bike, my wrists will be sore, my feet will be sore, my neck will be sore...not enough to ruin the fun, but definitely enough to get my attention.
On my LWB recumbent, after a full day's riding, my legs are tired, but absolutely nothing hurts. (Unless I got sunburned.) And it's more fun to ride than an upright. I find this bike the ideal touring machine.
You also asked how far you can reasonably expect to go on a recumbent. The answer is: as far as you want. If you get too tired to press on, you'll have to stop...but that's true of any bike. If, as you said, your legs never seem to give out on you, then there's no reason to stop riding until you want to stop.