In our old house we used 1x4s as "crown molding" to go with the look of the rest of the house trim. I'd do the ceiling ,then just cover the gap with 1x4 or 1x3 trim. Little fancy, almost no work involved, low cost.
I use 1x2 MDF for trim work in garage. Mine is all plywood so it works well for wall to ceiling cover. Even used it as trim around the workbench to give it a nice look.
Leave the gap, install crown molding. Use the gap to route your low voltage cabling (tv coax, speaker wire, Ethernet, etc...) and the crown molding will hide it.
