Would it not be much simpler to simply auction the girls? Establish a marketplace and “sell” to the lowest bidder. Boys would submit the lowest price (bid) they would accept as a dowry. The boy submitting the lowest bid wins her.
Of course prior to the beginning of the auction there would be a meeting of buyers and sellers (like a singles event), where the buyers (boys) can decide which products (girls) they wish to bid on. And the sellers (girls) can choose which bidder (boys) to approve submitting a bid for them.