I was trying to think of an inexpensive way to get from LEO to HEO when I came up with the idea of using electricity to move the satellite like an electric motor. The satellite is moving through the Earth's magnetic field, so if you put a big coil on it, you should be able to time the current through the coil in order to get the satellite to move in whatever direction that you want.
Then, I found that some one had already thought of it: http://en.wikipedia.org/wiki/Magnetic_sail
Quoting: "By varying the magnetic sail's field strength over the course of its orbit, a magnetic sail can give itself a "perigee kick" raising the altitude of its orbit's apogee."
In the simplest mode, you would energize the field to repel from the earth's pole as you pass over it. In this form of magnetic levitation, the satellite is going to want to flip over. You could compensate for this by having two coils extended on moment arms in a shallow "V" angle. See http://en.wikipedia.org/wiki/Dihedral This would prevent roll. You would need two more "wings" at a 90 degree angle to control for yaw. You might be able to get away with only three wings 120 degrees apart.
I don't know how long it would take to get to HEO. That would depend on how strong of a field you could produce over how big of an area. It would work better with a lighter craft.
This method of propulsion has the potential for reducing the cost of getting commercial satellites into higher orbits. Another advantage is that you can reverse the process to de-orbit your satellite at end of life. This method of propulsion might work to take you to another planet, too.
It seems to me that NASA would be interested in seeing if this works. I for one wish that NASA would do more proof of concept experiments like this with alternate methods of spacecraft propulsion.