My two penny worth.....
If the gearbox is full of oil there won't be any "pooling"
The environment inside the gearbox isn't particularly hostile.
Long periods in the sun is hardly "baking" and in any event grease would fair worse than gear oil, but the temperatures are not that high compared to the ratings for the grease and oil.
I have bought gearboxes from Leroy Somer that didn't require opening up to insert shims - maybe the gearboxes on the Santorin are different.
Drilling holes in the gearbox while still assembled is fraught with problems - hitting the gears with the drill bit, swarf from the drilling operation getting into the oil / grease...not a good idea.
Grease moving away from the gear is associated with the speed of the gears, not frequent or infrequent use. The worm gear spins quite fast.
if the oil / grease isn't required for lubrication, why is it there ?
Grease won't prevent water ingress. That's what the seals are for, and they should be replaced before they fail.
If you get salt water in the box, no matter whether you have grease or oil, you will have problems.