OK thankfully there was some low hanging fruit. If you bend off the mickey mouse ears on the switch, and there is a gap between the edge of the gang box and the edge of the drywall, you can screw it in extra (requires some creativity for the cover plate). Another similar option would have been to keep the mickey mouse ears and remove the drywall that they rest against.
Also you can edge the switch slightly left and right when you tighten the switch in, it's adjustable just barely.
Combining these things plus getting a lower profile (and wider) paddle switch (from RatchetFreak's answer) and opening the counter gap a tiny bit, I was able to get the switch just past the front of the body section of the fridge and to the left of the door, so the fridge wouldn't knock into it and turn the light off. And also closer so fingers can reach it. So nothing too crazy was needed in my case.
Another thing that would have helped is actually to raise the left front leg of the fridge (but not the right leg) (possibly adding a wedge at the back left) so the fridge tilted toward the front right (and slightly away from the wall). Because the switch was above counter-top level it bought a little space.
If I had needed more aggressive measures some more options may have been: grind down the front of the gang box a little (while still leaving some screw threads), and moving the gang box "in" a little (more recessed), by leveraging it out slightly from the 2x4 it's connected to, cutting the nail currently holding the box to that 2x4 (snips or hacksaw blade), moving the box, then re-attach it by screwing it from inside the box.
Thanks everybody, great ideas!