In addition, doesn't the process getting from GTO to HEO require some form of rapid acceleration? If yes, ion engines and solar sails are out.
The main requirement for escaping from LEO is that the engine thrust must exceed the atmospheric drag force. The time required to reach a HEO orbit mainly depends on how much electrical power you can generate, more power means more thrust and a faster ride to the desired orbit. A Cubesat power budget will be somewhat limited, deployable solar panels might help somewhat.
Most Cubesat launches are deliberately sent to low orbits to insure rapid reentry and burn-up to meet orbital debris requirements, that is why Cubesat launches to GTO are rare. A higher orbit will require a disposal plan, but electric propulsion can help with that too. Please see my paper in the 2012 AMSAT Symposium Proceedings.
Dan Schultz N8FGV