Use diatomaceous earth inside the home in addition to what you're doing. You say the cat is an indoor only. Mine, too. So, once you get the fleas at all stages out of the home, you should be free of fleas once and for all. If you can find some of my old posts, I explain how to use the stuff. Also, Google something like "non-toxic flea removal" and you will find lots of information about diatomaceous earth and how to use it. Some sites mention using it on the pets. No, do not do this. They should not breathe this stuff, and neither should you. It's not toxic, and it's not expensive. Buy it at a garden nursery. What you would do is apply it while the cat is taking its long day time nap. That way, the cat won't be getting near the stuff while it's in the carpeting and won't be breathing it in. This will work. I'm in a similar situation economically as you are. Plus, I have chemical sensitivities, and I didn't want to be using too much of that flea medication on my cat. Once I got rid of the fleas, they were gone for good. You will have to be vigilant for a while, but it can be done for very little cost. Diatomaceous earth is indeed non-toxic. It is just that it's a very fine particulate. You will want to wear a dust mask for yourself and keep your cat off of the carpeting and such for the two hours you need to leave it down on the carpeting. It works by desicating the fleas at all four stages. Diatomaceous earth is good for other insects and spiders, too.
Buy a fine-toothed flea comb at the pet store, and comb Fluffy every day. Between the Revolution and drowning any fleas you pick up with the comb, you should do all right. Be sure to vacuum like crazy, the carpeting and the furniture and all. Wash the blankets on your bed if you have the energy, but really, the fleas will be attracted to the cat and the Revolution will kill them.