The first thing to realise is that blossom end rot is caused by calcium deficiency. That’s it.
The plant needs to extract calcium from the soil, and that calcium needs to be dissolved in water. When the soil is too dry the plant can not extract enough calcium from the soil, and because all the water it can get is being directed to the leaves, all the calcium is also being directed to the leaves at the expense of the developing fruit. When the soil is too wet the roots literally suffocate and stop taking up calcium. So although overwatering and underwatering can lead to blossom end rot, it’s ultimately caused by calcium deficiency.
You will always get minor wilting at noon under those temps, but it should be disappearing by around 4 in the afternoon. While any wilting is to be avoided where possible, midday wilting simply isn’t a problem, so long as the plants recover once the temperature falls. If your plants are not recovering and are going into permanent wilt within 24 hours then your soil simply is not holding enough water. I have grown tomatoes when the air temperature was well over 35oC, and sustained wilting should not be occurring inside 48 hours.
You can increase the water-holding capacity of our soils simply by adding some gel crystals. These are cheap and they are available at any hardware store. Dig a few holes around your plants and drop in the crystals and the problem should be cured.
The over-watering problem is even more easily cured: don’t give so much water at once. Contrary to the advice you have received, the frequency of watering has little effect at all on tomato performance. It’s a myth. To the extent that is has any effect at all, the more frequently you water, the better the plants perform.
For optimum growth, a plant needs t meet evaporative demand. In simple terms, it needs to replace the water that it loses. However the water will only store a limited amount of water within the root volume before it becomes waterlogged. If that water volume is less than evaporative demand, the plant will wilt. It’s that simple. If a plant needs 2 litres of water a day, and the root volume will only hold 1 litre before becoming waterlogged, you only have two options: you can either over water and let the soil become waterlogged several hours a day, or you can water twice a day, giving a litre of water each time.
So rather than watering every two days, water twice a day if you need to, but give smaller volumes. There is no good reason not to irrigate at night, indeed most commercial operations do irrigate at night because that is when the plant is best able to distribute nutrients to the fruit. Without the laves demanding all the water, the plant can shunt sap and nutrients to the fruit. So if your plants are looking wilty when you get home from work, give them a light watering. You can afford to give a heavier watering in the mornings because the soil will dry faster so there is less chance of prolonged waterlogging, but try to avoid it all the same.
In the short term, get some foliar calcium fertiliser. It’s not all that common, but the better nursery supply shops should sell it. If you can’t get any, apply a complete foliar fertiliser that contains calcium. Because your root system is already likely damaged through waterlogging, you need to get calcium into the plant through the leaves to try to salvage the developing fruit.
Eggshells are a really lousy way to sovle the problem. They do contain calcium, but it is not readily available. So if your soil is actually calcium deficient (and it almost certainly is not) it won’'t alleviate the problem for at least a month and it won’t rectify it fully for 6 months or more. In contrast inorganic calcium salts will alleviate the problem within hours and rectify it fully within a week. However if your root system is damaged then rectifying soil calcium deficiency won’t alleviate the symptoms. But soil calcium deficiency is unlikely anyway.
A layer of mulch on the soil won’t hurt, but tomatoes are pretty water hungry, so the amount of loss form the soil surface will be minor. If you want to increase water retention then ad some gel crystals. It will cost about 3 cents a a plant.