Worried about excess rain

[dice]

Calcium moves fairly slowly through soils, so I would not add
more lime without doing a pH test first. If pH is still between
6 and 7, a couple of handfuls of gypsum on top of the container
mix is probably a better idea (adds calcium, will not raise pH).
Gypsum is fairly cheap at big box hardware stores (25-40
pounds for a few dollars) , really cheap at farm supply
stores ($5 or less for 80 pounds, usually), so it does not raise
the cost of growing tomatoes much to keep a bag of it around
for a pH-neutral calcium supplement.

Phosphorus stays put especially well once it is in soil or
container mix, too, so that is not likely to leach out. Nitrogen
is the main thing that you might need to add, and some
potassium. They need more potassium as fruit are developing
anyway, and a lot of people add more fertilizer that has
more potassium than nitrogen or phosphorus at fruitset,
even without excessive rain.

If you were using a liquid fertilizer soil drench, this would be
easy: fish emulsion for the leached nitrogen and molasses
for the potassium, ignoring the phosphorus. If you want
something that you can top-dress, something like a 5-1-5
to 5-1-10 would be about right.

Usually you want 6 hours minimum direct sun. Less slows
them down quite a bit (although you are pretty far south
so you might get away with 4 hours; I would not know
whether to expect that to work without having tried it
first).