With regards to the etiquette of when you can drop people's names into the conversation, I would ask somebody over there in the Valley as my understanding is there are thorny social norms there and I'm only barely conversant on them.
With regards to expressing urgency, maybe something like: "I appreciate that you've got a busy schedule. Boy, can I empathize, it seems like I have to slide the actual running of the company in between the fundraising. But, you know, the market's the market right now. I'll tell you the same thing I'd tell everyone else: we'd be happy to pencil you in for X but our situation is evolving and there may not be an open window for this by X."
(I've never raised money, but when I sell consulting gigs, I typically throw in a true observation like "I have N weeks of availability. My experience is that I usually book up." Ask the 500 crew, but it seems to me like "We're a 500/YC/etc startup. Historically, the rounds sometimes close out quickly." is absolutely true, conveys urgency, leverages social proof, and doesn't say anything you wouldn't want retweeted.)