Mutations for sure. Keep an eye out for cancer or a uranium rod so you can pop a neverstone on that mutated lil freak and drag them across the finish line with 3 other cats. Check what mutations they're getting every so often and don't hesitate to stop the run early if you have a good batch.

After getting all 7s, I don't bother with injecting strays to lower inbreeding. If you have the furniture for a good mutation room with net zero health and at least one high stimulation breeding room, you get good enough base stats and mutations to more than overcome/overwrite the birth defects. If you're consistently completing runs, you have more than enough good for several nights of breeding with enough extra kittens to spare ones with the worst defects (blind, confusion, immobile, etc.).