Have the walls opened and the vents loweed a few inches--this is not too big a job for the right pros--and realy the only way to go if you are going to install crown molding. Also consider real plaster moulding which has many advantages.
PyramidDG.com

The pop out looks like a realistic option. Would purchasing a new vent and carefully reducing the size from the top down to allow for the installation of the crown moulding be an option???

Can't really comment on that other than to say vent sizes are designed on room size, changing could reduce efficiency of heating and air of that room.
Do a few mock ups of the crown pop outs of various sizes to see what you like best otherwise your going to need to open wall and extend vents down like other comment suggested. Good luck !

My painter showed me a great solution. He merely "slotted" the c/m to permit it to fit perfectly to the wall. The possibility of minor efficiency issues may exist, but the temperature changes in California are not extreme.

Yes I used to do that but it didn't look as good as the pop out solution I came up with but if you decide that's the way to go and like the look then good for you with finding a solution to your problem. happy remodeling