Town won HP b/c of good scum-hunting and then investigation. I don't recall the houses being a factor in that. chairs and I are not in a Greek house, btw, so we don't know what kind of discussions are happening there. In HP there were 4 houses, 3 scum, and 2 factions. The 3 scum by chance ended up in different houses (town didn't know that, of course), so they knew the composition of each house from the beginning, and claiming meant everyone had that information. In HP the houses had voting powers, so there was potentially more pressure on the scum in each house, and opportunity for scum-hunting through the house voting discussions.
Here we have 3 houses, an unknown # of factions and unknown #'s of members in each faction. It's not clear if town wants to win the challenges or not, and the knowledge is pretty specialized, so it shouldn't be hard for scum to blend in.
ashersky: will flips contain the individual's frat/sorority?
It's not clear from the OP how the prizes work -- if one individual gets the prize, or if the house votes on a target for some prize action. The winning house from the first challenge knows how it works, though. They might even know what the prize did!
I think that knowledge is enough for me to advocate house claiming. Let's hear from more people first, and then if it looks like a go, I don't think we need any special order or system.