You are dipping to deep in the pan if you are getting paint on the roller frame---
just get the nap wet--not the end caps or frame--also--use your ears when rolling--you will soon learn the sound of a properly wet roller--the sound changes as the roller runs dry---or you are over working the paint.
Also learn the speed for proper application--the paint must flow out of the nap--roll to fast and it's not going to cover because the paint can't flow out of the cover fast enough.
New members: Adding your location to your profile helps in many ways.--M--
On a 12 x 16 foot ceiling, I would roll 2 8' sections along the 16' length. You would start by putting the fully loaded roller not exactly at an end, but 2 or 3 feet in. Roll from there to 8 feet out. Then roll back and when you get near where you started, there will be a thick load of paint that you can roll through to complete the first couple feet at the beginning. To do the second section, do the same thing - start a couple feet from where you left off, then when you roll back, roll right through into the first section and roll the roller slowly away from the ceiling after overlapping so you don't see a start or stop point.
I'm not really sure what you're using the 4" roller for, because unless I missed something you don't need it. In any case, I would not be dipping it, I'd be rolling it in a pan.
Edit: OK I see you're probably using Toolseeker's technique. Well, that does work although I just cut in everything. I can go very fast in wall corners with a brush when I just have to paint, and not really cut in. Then even with a 9" roller you can get very very close to the edge, so I don't find brush marks to be an issue. Dipping works with a "corner roller" once you get the hang of it.