As was stated, there is probably a reason that the drop ceiling was installed. In which case, you will probably have to build sofits around whatever obstacles there are. A little bit of extra work but if you have a little carpentry experience it should be too much of a problem.
Crown is a good solution for the gap between wall and ceiling, but if you want, as long as you cut the drywall well, taping and mudding shouldnt be a problem for those corners. I usually do crown though if the look is right for the room. Because there will be no support from the wall to help keep the ceiling up at the edges, I personally would do strapping across the joists and make sure to sink plenty of screws. In my area, 5/8" is code for drywall on ceilings. You may want to do that as this helps prevent sagging.
I like the channel idea as jeepcop stated I have just never personally done this...great idea through, sure it would work if you can do it.
Hope that helps.