Avoid the ‘daytime’ watering. I’ve even seen people claim leaves can be scorched by water evaporating in intense sunlight but I’ve never seen it.
You want to make sure that the water goes to the plants not to the atmosphere so the cooler the better and I’m guessing that early morning is cooler with you than even late evening. But it also depends on how quickly things heat up. You want to give the water a chance to get down to the roots before the sun gets too intense and the rate of evaporation rises. It would be nice if that same water had a chance to actually get into the leaves before being sucked out again too. My parents, experienced gardeners, aged 73 & 74, water late in the evening (unless they’re having a real heatwave when it’s twice a day) I’m pretty sure that if they thought early morning watering was the solutiuon they would be doing that instead. (Afternoon naps would make up for early mornings )
Also make sure that the plants get a real good soak not just a token sprinkle - this means a lot of to-ing and fro-ing with watering cans, also think about giving the ground a quick rake to make sure the water doesn’t just sit on top of hard dried out soil.
(I just have pot plants, the earth dries out quicker and I can stick them in a tub of water for emergency de wilting or at least put them in the shade until later but I guess you don’t have that option?)
Question - what type of plants do you have ? If they are imports is it possible that you could start replacing some of them with ‘local’, less thirsty, plants ?