Ok, by many of your assessments I'm an old bugger. My knees used to be classified as done. Since riding fixed my knees are much better due to building muscle around them. I don't lay long patches of skid, I skid in small increments TO SLOW DOWN. If you want to just lay long patches on the ground go buy a bmx.
Reason: my bike is adjusted properly. I have the right fit. I would bet that your saddle height is based more on style than function. Your gearing is probably wacky too. Click on search, get the gearing for spinning and get your saddle height right for your femur and tib/fib length. Adjust saddle height then report back on a month.
And go buy some ibuprofen.