@Nat C.
No: to do that is still to be primarily focused on cost and price. Focus on quality. The quality of a contractor's work is a reflection of his character. If he is conscientious enough to care about his work and his clients, he will be a person of integrity. Ask around...look at their work and how they manage their business. The good thing is: once you find such a person, it will lead to other such persons (birds, feathers, flocking, etc).
A contractor such as I describe will not necessarily be more expensive but if he is: so be it. It costs what it costs. You just have to factor that into your equation. For example: with most of the subs I use (electrician, plumber,etc) I don't even price shop. I've known them for years and trust them. I'm sure, in some cases, I could probably get the work done for less but I don't care. They do what they say they are going to do and the work is done right. No headaches; no stress.