In central FL here, and tend to hatch all year the last 3 years running. So I really understand your concern.
Last year I had eggs in the incubator during a heatwave, the temp kept rising above 100F so we had to keep taking the incubator lid off to cool them down.
This is what an experienced broody does when it's hot, she stands up. But a lot of first-timers, or broodies just lacking a full set of instincts, they won't stand up and they cook the eggs.
We've learned not to have the incubator inside during summer because the way we run the AC makes it too hard for it to compensate (the "drafts" not just the temp). So I have it on the porch once the cool weather passes. If we had an indoor room without an AC vent, that would be better.
That heat-wave brood had 4 crossbeak chicks in the batch, though I hadn't had any pop up in my line in the years before or in the hatches since. So I put it down to heat damage.
Winter is a much better time for us to brood chicks. I try to do a lot of winter hatching when the hens are cooperating with eggs. We get those last intense heat waves in October, but in November they don't spike as high and that's a good month to begin (with an incubator, broodies won't usually comply that time of year).
When you're providing artificial heat with brooding, the harder thing to manage is overheating. So we make sure we have a nice long brooder and the heat source at one end so the other end can be cool. During warm months the heat sometimes has to be cycled off and on so that's a lot of extra monitoring of the chicks and what I consider "hard" (relatively) brooder care.
Although broodies can be a lot easier, they can also make it harder. I just did a big spring push to make up for the upcoming summer off, had 4 broodies going at once, and I'm telling you it's not like just fixing one more plate at dinner. It's like having 4 separate meals going. I didn't have the same great results with them this year that I've had previously. Even my most experienced broody crushed a hatching chick. I lost 3 more under various hens. And a bunch of eggs that candled as developing never hatched. It was unusually stressful.
In the past I've enjoyed letting broodies do all the work. But if the time of year doesn't work, I say just stick 'em in the incubator and raise them yourself. In June the real heat starts so I think you still have time if you start now.
* You mentioned a concern about rain. Is the area you would brood sheltered?