I've worked with a couple designers on this project, and wasted a lot of time and money, and they still didn't get it right.

Can you be a little more specific? What makes you think they didn't "get it right"? Did they target the wrong audience? Did it convey the wrong message? Was it not memorable or unique?

The reason I ask is because a lot of clients don't really understand what designers do. A designers job isn't to satisfy the clients personal tastes and opinions. So, thinking about things a little deeper, could it be that perhaps you're wrong? Maybe they crafted you something based on their expertise and experience that's perfect for your needs and you're having trouble seeing past your personal taste.

People don't go to crowdsourcing websites to look for an expert that will solve their problems (and identify ones they didn't know they had.) People go to crowdsourcing websites when they think they already have the answer and they just need someone to "draw it" for them because they "aren't really good with Photoshop" (professionals don't design logos in Photoshop.)

Maybe I'm off base here. But as a designer that works with a lot of small clients on branding projects I can't tell you how frustrating it is to try to help someone that doesn't want it. Sure, ignore my advice. I've only worked as a designer and art director for 15 years, went to school for design and worked beside amazingly talented people on projects for some of the largest corporations in the world. But no, you're probably right, I don't know as much about my field as you do.

I spent an entire weekend filling out their branding questionnaire.

Keep a copy of that. If you work with designers frequently you'll be asked those same questions over-and-over again. Eventually many of those details will end up in a style guide if your company grows to need one.