Perhaps a railgun plus a skyhook? Railgun up the side of a mountain on the equator and an orbiting station with a capture mechanism that is in a sense the strongest bungee cord imaginable. 17k mph is a lot of speed to make a grab. Exiting the railgun at mach 3-4 at 30,000 feet has engineering issues and still has accelerate above mach 20 for a stable orbit.
Laser propulsion is an interesting / wacky idea. Don't know if it would actually work, but the core concept of keeping the energy source on the ground is an interesting one at least.