The person who said about the goldfish, is a good idea. Buy try buying feeder guppies or feeder goldfish. You get 12-15 for $1.00 & they'll last long enough to eat the mosquitoes. Some might even live long enough to become pets.
Please do not put chlorine in your perfect Rainwater, go to the pet store and buy a couple goldfish a little container of fish food generally goldfish don't live very long but I had my last 3 years until the raccoons got them, when the rainy season starts just keep them in a fishbowl until you can put them back out.
To keep them from going back in, make sure to cover with screening, the water can get in but momma mosquito can not. We change the water in our birdbath daily to prevent mosquito colonies.
Churning the water sounds like it would work because mosquitos only lay their larvae in standing water. You could skim them off too and squish them (gross but gets the job done).
I've always heard that churning the water drowns the larvae. This would be better than using chemicals. try churning the water for a minute every day. Also try covering the top with a board during dry weather. This will keep any bugs inside.
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