Don't over complicate things. People just need a price. How you get there is academic and if it's not based on what you need to make a living what's the point?
To "take care of the minimum charge" why not set a minimum charge based on the minimum amount of time you can get in and out of a job and what you want to make per hour? If you're old and slow like me and you know you're going to be there for at least an hour, if not an hour and a half, and you live in a high rent district like me and need $100/hour or more, set your minimum at $125. If it's an issue when they call tell people your minimum is $125 and let them worry about it. If the job is close, if it's a repeat client, if you're sitting around twiddling your thumbs you don't have to beat them over the head with it. You can waive it. It shouldn't be an issue that often.
Several years ago I knew this fellow, D i c k Ragan, was crazy because he was telling us we should all be charging 50 cents PSF. I knew no one would pay that much for carpet cleaning. That is, right up until my wife gave me the ultimatum of "we need to make more money or I want to do something else" and we started to raise our prices. I'm a slow learner so it took a couple of years or so but I did finally realize D i c k was right.
These pricing games we play in our heads are for our benefit, not the customers. They just want a price. They don't value our service the way we do, chances are they value it higher than we do. We wouldn't pay "this much" for carpet cleaning and project that assumption on our customers.
People will pay for the things they want. When you see families in nice neighborhoods with $70K plus of automobiles in the driveway, big screen TV's, pictures of their cruise and skiing vacations, nice furniture, kids in college, so on and so forth they're telling you they have both the means and the desire for nice things, things that make them feel good. Clean carpet makes a lot of people feel very, very good.
We learned the hard way you'll never know what the market will bear until you push the envelope outside of your comfort zone and have the guts to stick with it. You don't have to repeat our mistake.