I've damaged two of the carbonator caps by over-tightening.
The more headspace in the bottle the quicker it carbs when using the cap. I do 1L and 2L bottles so can definitely see just going this route if I didn't already have kegs etc... It's real easy to get a feel for how much co2, the psi and volume of headspace carbonates the beer with shaking. Usually I'll give the bottle 3 successive blasts @40psi with shaking in between.
But first squeeze all the air out of the headspace. And it helps if the beer is cold.
In regards to bottles- I'll start cracking them on day three and sometimes they go into rotation then or I have to wait a bit longer like a week. How else does one learn about their beer. Not like beer is something sacrosanct that can't be touched.