We used to do this back in dino days. It is Green Book permissible. The fact of the matter was that it was partially 1) to snap up the women and 2) to up our numbers. We were small and this option was mostly offered to women who already knew most of the chapter but for one reason or the other weren't able to pledge when the bid was offered, but did want to "declare their intentions" with us. For the most part it did work, but then there were a couple women it didn't work with plus the Greek life director said it was hazing (which is bullshit but whatever) so we stopped.
However, if you have women ACROSS THE BOARD requesting this option - and not the sororities offering it - for monetary reasons almost exclusively, that means dues are too high for the campus. Something's got to go. I know people don't like to hear this but if the house is killing you get rid of it. Try a block of apartments instead.
I also think that deferred rush would solve a lot of your problems. If I was a brand new freshman on a campus with that male/female ratio I'd be clinging to my girls every minute too. They need a semester to relax and get to realize that dudes are just smelly and gross.
