yes, yes, and yes.
I Set and forget and over pressurize .
Get 90% of carbonation complete in 3-5min using over pressuring, say target 8psi then dial up 20psi wind the reg back off and shake, watch the dial fall back as you shake, you get an idea of how close you are to the target carbonation by how quickly the keg pressure drops off, as you get closer reduce the over charge pressure to say 15psi , shake , 10 psi shake , etc... winding the reg back before each shake. Give it a go and you pretty quickly get a feel for it.
Next set and forget, 24hrs at you intended pressure and your done.