As long as it is light tight it's fine to remove the fill cap. The bleach is the step that requires venting.
As to agitation, "normal" C41 development done in commercial labs is a constant agitation process of one type or another.
When I started and used hand agitation I used the method you described and put the tank back in the water bath between agitations, worked ok.
As I refined my developing process with a larger bath I switched to rolling my floating tank constantly on its side in the water bath. I was using stainless tanks so had to gently keep the lid on worth my fingers, roughly 1 rotation every 2 seconds worked fine for me. Be consistent.
Developing, as I'm sure you know, is time critical both directions, so 3:15 unless you are pushing or pulling, I start the clock as soon as I stop pouring, I start dumping at 3:00, at 3:15 I start pouring in the bleach.
The bleach and the rest of the processes go to completion so the times suggested are simply minimums, extra time, say doubling, doesn't hurt a thing.
For the bleach in hand tanks I did not lay the tank on its side, tilt and spin were the motions with the fill cap off. Your stir stick with the occasional tilt should work fine.
Fixing and final rinse/stabalizer can be done either way, cap on.