How can I temporarily secure a wooden countertop to its base with limited cabinet access?
Use figure-8 clips. Screw them into the frame overhanging the outer edge (they are usually done to the inside, but outside works fine, and only your friends who have reached &quot;lying on the floor&quot; will ever see them, and that, blurrily.)

You screw them down into the frame, up into the top. It's what they were made to do.
Alternatively, borrow, rent or buy a pocket-hole jig and put in new pocket holes on the outside of the frame (just like the ones you have now, on the inside of the frame) Once again, counter overhang should make them unobtrusive to anyone not lying on the floor.