I think the CATS are the real issue, and I doubt that even flea-bombing would solve the flea problem.
My yorkie has severe flea allergy. Even one bite can lead to severe skin irritation and constant scratching.
I found it a challenge to keep him free of fleas, and I am sure that it is our cat that keeps bringing fleas into the house and surrounds!
Pepper has some other health issues, therefore I can't use chemicals or flea tablets on him.
Therefore, the cat is treated monthly with Advantage, and once a week he takes a Capstar tablet. At least once a week, the whole house is being thoroughly vacuumed, and bedding is washed (and sometimes also sprayed).
I can keep the situation reasonable under control. But have to be very consistent in my approach. I have tried alternative methods, but none seem to be effective. I have given up.
Do you know the owner of the cats that are coming to your property? Maybe you could talk to them (if they look nice and approachable)? Ideally, the owners themselves would treat the cats. Not sure if they would agree to you giving cats treatment... Probably not. I believe COMFORTIS is the most efficient treatment, and now also available for cats. The tables are supposed to be incredible, have an instant and prolonged kill effect on fleas! I have read that this medication can have some serious side effects on the pets, though. Otherwise, I would have given it to Pepper (should not be given to pets with history of seizures, I believe) or our own cat.
Other suggestions to look into:
* use of diatomaceous earth food grade on the outside bedding (maybe also in house, but be very careful with inhalation of powder! Extra research recommended.)
* ways to keep cats away from property
maybe there are suggestion on the internet?