No help to you but i grow mine in a greenhouse and its humid as in there. Gets watered every 3 days for 30 minutes. ive never had an issue with what you have mentioned though. My cheery tomato plants were about 5m tall (i grew them to the roof then sideways across the top of the green house, and my standard tomatoes were about 4m tall (same deal).
I get about about 30kg's of tomatoes off 6 regular plants and 4 cherry plants.
Do you grow them in the ground or in containers? Anything in particular you do with the soil?
in the ground in beds in the greenhouse. i grow them from seeds.
nothing much to the ground, my own compost, some sheet pallets and some blood and bone, and then some liquid tomato food and some granular stuff as they start growing.
I have a irrigation timer in the green house the goes for 30mins every 2nd or 3rd day (can remember which) at 6am in the morning, and all the head are about 20cm from the ground so they spray the bottoms of everything in there.