Given the state of the BG frenzy, I think a few things need to change. First, it shouldn't be fastest fingers/connections gets the BG. It should be a random lottery. Second, I think they need to pre-assign the lottery process so you know before showing up at DHS whether you will get a ride. Perhaps by say 5PM the day before, you have to enter your party in the lottery and you'll be notified if you receive a BG and what BG you received by say 6PM the day before. Third, for those staying onsite, perhaps with at least an 3-4 night stay, you are should be guaranteed a BG and you can sorta list your days of preference in advance and Disney will assign one to you. This way, you know when you go to DHS, that you will get a ride.
Or just scrap the whole concept altogether and go stand-by only and how long you are willing to wait determines who rides. The problem here is how to prevent people from continually showing up earlier and earlier. I will say, though, as someone with young children, I do not favor this alternative, but at least you can't argue with the equity of such a system.