Ease up on the running and sit-starts on problems, maybe do some low impact cardio for a couple of weeks, see how it feels.
I would try some light bodyweight only ass to grass squats (try them with medicine balls if this feels ok), wobble board squats, and a load of leg extensions, do you do any leg specific training at the moment?
If you don't have them already, get some decent orthotics for your running/gym shoes, makes the world of difference to your long term knee health, also helping you transmit power more efficiently through your feet.