The sling shot effect is there but it isn't very strong.
If you are willing to play only single player, you can go into the assets directory and play with meleeparameters.xml
These parameters will eventually get put into an .ArenaXML file but for now, you can mess with them directly.
Another file you can play with is StarControlGalaxy.xml which is in the Galaxies folder.
At the very end of the file is the Solar System that is used in Super Melee which, needless to say, has 1 planet. You can change all kinds of things there including adding more planets.
We are working to make it so that you can create and share your own areans (which will have the solar system you're playing in). but if you can mess with it here.
Note, if you change this, you won't be able to play MP until you go and do the Steam reconcile files thingy.