Joe,
With respect, you're making the basic mistake of thinking that the only way to compete with these people is on price and are prepared to forgo quality in order to do that. Do that and not only have you got, 'one shot' cleaning, you've also got 'one shot' customers, 'one shot' being that you only see them once.
The business objective is to build a loyal core of customers who consider you 'their' carpet cleaner and that only ever comes about, not through being the cheapest, but through the sheer quality of your work. If you make price the only issue upon which people can choose you then be prepared to do price battles with these people ad-infinitum and if you do that they and not you are running your business because they are in charge of your prices.
Simon