Would there be some way to get around this by keeping some of the propulsion system earthbound? Like a humongous slingshot or catapult?
Yes. See my post #10.
The biggest hurdles for that approach have to do with the fact that any ground-based boost method will induce high accelerations; and after that, the payload ends up having to go very fast in thick atmosphere.
The only way to handle the first problem is by adding length to your booster system. You'd have to handle the second by adding sheilding (heavy!), or somehow keep the atmosphere in the launch system at low density.
There is potentially a lot of merit in developing an air launch capability, although that's got to deal with other issues.