I'd say, forget the price tag and look at something else, escpecially if you're short on time and money. Great communication across domain boundaries is absolutely crucial, and that involves the way you communicate as well as what partner you pick. And if that works great, it's very, very likely worth whatever they charge you.
People who are not familiar with a domain can talk a lot of rubbish that confuses a professional and produces bad results (the man who cuts my hair is great because he totally ignores what I say). On the other hand, professionals that don't take extra care to get every detail of what their client actually, really wants, won't be able to do great work.
For example, I paid twice what you did on my logo (3,600 €), and was totally happy. On other occasions, I have paid half that on a complete web UI, and it was an utter waste of time and money. One reason why my logo and CI were relatively expensive is that I hired an agency, not a single designer, and that meant I had two (!) people who interviewed me intensively about my business, my goals, my product, my attitude etc. and then translated what they thought was relevant to three independent designers who ran as many revisions as were required to make me happy (about 50). And I didn't get to talk to the designers until very late in the process when we had established enough understanding on both sides, that we could communicate efficiently.
Note also that I'm not saying expensive is better. I have a great accountant and tax consultant who is way, way better than more expensive ones I've tried and I chose her because of how communication worked. The best laywer I've ever hired charges 70% of what the very worst lawyer I've ever hired charges.