What was the original tire size on your Schwinn? You say you used to have a 24" rim with a thick brick tire back there, but still rubs. Do you know anyone with a welder who can cut you out a doner set of rear dropouts and then weld them to your exsisting dropouts, because that is the only was I can see making more clearance in your frame for your tire. It is kinda tricky and you gotta really get a good weld in there and have everything measured up right, but if done right, you can effectivly move your rear wheel back an inch or so, but in doing so will lose the ability to mount caliper brakes on the rear. Note: i'd only have an experienced fabricator try this, or someone with more than their fair share of common sense.
Sorry no pictures. Other than that, you could use your set up on a 26" frame, perhaps. Hope it helps.