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.
It would allow patrons who fail win a BG to decide if they are still interested in using their ticket at HS or if they'd rather try to transfer their reservation at another park without having to spend their (rather expensive) ticket somewhere they may end up not even getting a coveted BG (possibly their who reason for visiting HS to start with).
While this is a great idea, this is exactly why they would never do it. A pretty good group of guests simply wouldn't show up that day if they knew there was no chance to get on Rise. They would try another day if they could, and if they couldn't then it becomes a massive guest satisfaction fail before they even step foot in the park.
I have no idea how you fix it, honestly. Knock out some of the parking lot and build a second building. They've already got the blueprints done up...