All of these questions are hard, actually.
As far as judging the quality of an EE when you're not an EE: You will have to be able to communicate well throughout the project, so even if you don't speak that much Electrish, you should try to ask questions in their language. The other way round, EEs who talk so much Electrish that it sounds like they know all and you are dumb, well, they may be bright, but they will not solve your problem. You will have to spend some hours in your first meeting and if you don't even get the least idea about what tricks they are going to use to get your requirements running, you should not sign any contracts.
Some side-notes: I'm not from NYC and I don't know about an online list, but for jobs as special as this one, It may be the case that no yellow pages (or the like) are available, no matter if you're from Europe or from NYC. My company often arranges contracts with smaller companies for R&D tasks, and it really is very difficult to find good partners. Often, the less shiny and power-pointy ones are the good ones. Once you found a shop who looks like they might be able to help, prepare some good questions concerning your project and try to ask like you're the employer in a job interview without being impolite.
Good contract developers are real treasures. Word of mouth might be the only source towards finding them.