Two comments for you. Deflate the tube as much as possible. Reinsert the shrader valve with tube collapsed. Next get some baby power / talc and liberally put as much as possible in the tire and wheel so that everything becomes bone dry. Then sprinkle a lot on the tube. Then it will go much easier and when you add air, the tube will 'unwind' itself inside the tire/wheel. This is a standard method on general aviation aircraft tires. There really is no other approved way. The remaining talc powder will continue to absorb moisture. Surefire way to get longevity out of the tire and the tube.
Adding a couple tips. One we all have duct tape, reline the wheel with it. It never hurts to add some extra so future rust flakes dont interact with the tube. Second and I dont see anyone doing this. Attach a strong string to the new valve stem and route it through the valve stem hole. This way you can just pull the string when the tub is inside and the valve stem will come right through the hole. You still have to have it somewhat inline, but its so fast and easy. Last tip is inflate the new tube then release the air and reflate. This will make sure the tub is sitting correctly and not overlapped on its self or bound. That way you do weaken the tube.
I did that and all good until I put air in the tire -- the valve stem popped off the tube, i put another tube and it popped off again--- went ahead and bought a tubeless tire.
