"Also, it's been my experience that clients care about the price before the project begins, but never after."

I agree, and from both sides of the table. I've provided added services to projects where the total value of the added services were a multiple of the initial cost, without getting any complaints or requests to lower the budget. I've also paid many extra hours for additional work and never felt bad about paying for any of it; and I'm very cost conscious and drive a hard bargainer when I get an initial offer.

I think it's a trust thing, after the other person has shown that they're capable of providing high quality services, cost is not so important any more, while if you're just getting quotes from people, you have no way to find out the true qualities of the people you're asking (usually). Even references from people you know personally sometimes end up blowing up in your face, a guy may be having a bad day when he's working on your project, screw up and refuse to fix it. Relationship-breaker right there, while he may have done an (objectively) great job at your brother in law's project last year.