You get Bones on the line instead and tell him about your current situation. He fills you in on what everyone is doing and adds that some detestable frogmen from the Green Room have been taking out all of the doors that lead to it. Jeeves is now out of stock.
He was able to get Dealer's limp, punch-tossed body through another door, but now he needs someone else to lead those Pure Selves into it so they can be taken out. They won't take the original bait now, and he can't do it himself because he needs to keep watch. HD volunteers himself for the job, saying that he can round up the other boys and make quick work of the matter. Bones sighs. He'll trust that, since Defalcator vouched for him.
You note that you still have your Slip n' Slide. If Bones can tell you when to stop, you could theoretically get yourself into the Green Room and meet Sharper and Dealer there. You'd need a lot of slip to slide on, though. Bones tells you that the staircase you're at doesn't end, it should suffice. He'll track you through the hotel's map and let you know when to hop off. He then hangs up on you and leaves you to it.