Rabbits that aren’t able to clean themselves (due to illness, old age etc.) are more prone to attracting flies coming to lay eggs where it’s moist and warm (e.g. the rabbit’s rear area). Theoretically it only takes one fly to cause flystrike, but I think there’s no need to freak out yet as I’m sure there are many rabbit owners who have had flies in their houses and the rabbits were fine. Just keep monitoring their poop and behaviour to make sure everything’s okay.
Your cleaning schedule doesn’t sound TOO bad. In some areas flies only appear during a particular season, so if that’s happening in your area then maybe you could clean out the cages more diligently (daily?) to deter them from the bunny area.
I’m not sure about products, but in my area flies don’t really appear unless there are stuff like unemptied, open trash cans or anything dirty (like rabbit pee and poop), unsealed/uncovered food etc. As long as the house is kept clean and there are no conditions suitable for laying eggs, they would naturally go somewhere else. For existing flies, you can probably get those electrical insect killers or swat them with something then clean the area thoroughly.