If I ever hire an engineer for my business -- I hope it'd be someone I've already worked with and know -- but if it had to be someone random, I'd pursue this method:
1) Solicit Resumes
2) Pick N candidates
3) Phone screen to make sure they aren't complete assholes
4) Stack rank & pop top candidate
5) Pay them to develop a feature on contract
6) If satisfied, repeat step 5 until ready to hire; else repeat step 4.
I think it'd be important from the start to let candidates know they might need to do a week or more of work (for pay) before getting a final hire. Some people would be put off by this, sure.
But I suspect the people put-off would be people desperately seeking full-time employment. I think it might attract a lot of talented people that don't want to go through a 4-week long ceremony of an interview process that takes up days of time with no pay, though.