There is long term plans for an integrated game example, but I'm currently busy most days with paid work, so I'm not totally sure when that'll happen.
The physics example could be turned into a platfomer game pretty seamlessly though!
You can solve the "slipperyness" by only resolving the collision in the upwards direction for slopes. It'll be tricky if you're not familiar with vector maths, but then anything to do with slopes will be, I'm afraid!
If you ask for help on the love2d discord I, or someone else, can help you out more there.