Having put up most of my drywall, I have left a few gaps that are too
big (for instance, next to my plastic electrical boxes). At least one of
these gaps is at least 3/8" wide (and 4" long). My current plan is to
"glue in" a small block of drywall using my heavier joint compound, and
then build that up--allowing it to dry in between layers.

Is this approach likely to be successful (w/tape?)?

Thank you for your thoughts.

Bill