If we were to organize this seriously, I would do it this way. We have plenty of men... Right? I think it would be logical if each girl nominated 2-3 candidates (without repeating!), and предварительно asked for their CONSENT. I think this would serve as an initial selection process in a way ;)
Then we can come up with what to do with the "misters" ;) We can definitely come up with some tricky ideas :D The main thing is that if something doesn't work out in the first stage, there's no point in discussing this topic further, IMHO!