Re: drywall between exposed ceiling joists
Sure it can work and be visually appealing --- depends.
Personally I like to see wood elements as part of the features .
At times when you show appreciation and celebrate parts of the structure it can be stunning. However , for me personally, too much wood can be drab and needs a different surface like plaster or drywall that is a pleasing contrast.
Redwood is a beautiful wood. You will definitely will want to ensure it's nice and clean along with being oiled since it will be exposed.
Now depending on the room will determine how your idea will look.
If the joists are 16 inch on centers , scale of the room and a low ceiling height this may end up making the ceiling look too busy. On the other hand the exposed joists can offer the sense of height as well.
Here's the part where I'm a little confused about ---- the joists are 2x10 and you mentioned only having 2 inches exposed.
Again depending on the room , if you had as much of the depth of the joists exposed it may be more appealing.
Using the J bead will make a nice crisp edge and look good providing you take your time making nice straight cuts. After all , the bead will follow your cut and there is only so much it can do to hide imperfections. So , if the drywall is tight at one end and you have a 1/4 gap at the other , then your messing around with caulk.
Many folks have difficulties visualizing concepts --- perhaps try painting a couple of spaces between joists with white paint to get a feel of how it might work out.
After all, paint is pretty cheap and relatively easy to put up.
"" an ounce of perception -- a pound of obscure "