I am attempting to seal gaps and cracks in an apartment kitchen. Upon inspection of the sink area I noticed a void approx. 6" wide between the cabinet beneath the sink and the adjacent (tiled) wall. I was able to remove a fascia piece from the cabinet in order to get some pictures inside which revealed a 1-2" gap where the drywall simply ends short of the corner. This gap is exists from the floor up to the sill height. I want to fill in this gap effectively to prevent pests. The end result doesn't need to be seamless but should be possible to paint, i.e. no unfinished drywall or foam which can harbor mildew etc.
The ideas so far:
A: The building super's solution was to board up around the countertop and cabinets so that you couldn't see the gap and debris couldn't accidentally fall in which doesn't really solve the issue of pests being able to enter/exit through the wall.
B: The next thing proposed was to use spray foam such as Great Stuff Big Gap Filler. This is quick and easy to do however it would have to be done in one shot and cleanup afterwards would be impractical. If going this route, I would like to have a board or other flat surface for the foam to set against instead of spilling out of the gap.
C: Patch with joint compound, repair fabric, or cut drywall. This seems difficult with the limited access (I am told the cabinet must not be removed) and I am unsure if a backing material would be necessary.
D: Simply use a large corner bead such as this 2-1/2" one sold by Home Depot. One side would need to be affixed to existing tile, the other would hopefully cover the entire gap distance on the drywall side. Might need additional backing material?
I have read similar questions on this site (ex: How do I fix a hole/gap between my shower tile and the dry wall next to it? and How to finish wide gap in drywall at edge of ceiling) which offer very suggestions similar to C & D. However limited access is my main constraint, so it is not clear whether these options are effective if I am unable to cut a drywall patch or cleanly caulk the corner seam.
In summary, given the situation are any of B, C, or D obviously a better solution? What gotchas should I be aware of and how can they be accounted for?