I'm looking for a motor and battery set up that can last for over an hour and spin the propeller at 6000+ rpm. The propeller is a 28x20 single blade being connected to a second blade for a total of 56 inches. The weight of the whole propeller is 0.56lbs.
The first issue with your question is that you can't spin a 56" prop at 6000RPMs without it tearing itself apart. The tip speed of a 56" prop at 6000 RPMs is 1000mph, well over mach speeds. Practically speaking a 56" prop will probably be good up to about 3500 RPMs safely, with an absolute maximum of about 3700 RPMs (0.80 mach).
56x20 is massive, so you're going to need a significant motor. Based on the specs and what you're looking to accomplish it could vary some, but this motor is probably very close to what you're looking for: https://www.getfpv.com/lumenier-lu15-ii-80kv-professional-motor.html The 40" props they've tested are only hitting about 3500 RPMs, and barely within the motor's wattage limits, so you will probably not quite be able to hit the maximum RPMs for the prop, but should be workable.