Stop dancing around, don't keep your cards close to your chest and stop with all the intrigue!
Selling consulting services is a process, not a trick to fool them into buying. (Closing techniques are for doormen) They either want to move forward or they don't. And if they don't, you probably aren't going to change their minds easily. (E.g. you've already blown it)
So when you are all sitting there, the meeting is drawing to a close, and you are ready to walk out. Just ask the question!!
"Whats the next step?"
You are there because you want to sell to them, right? They have listened to you because you might have something of interest to offer them. So make it clear.
This isn't charity, you are there to sell the service or product. They are probably interested in going forward but not sure how, so clear the air and ask them.
Where do we go to from here? is there a small piece of work that could help move the larger piece forward? Can we meet with the person who signs the cheques?
You are their co-conspirators in this process. You are all working towards what is a better future for the company and you will achieve more working together than trying to second guess everyones intentions and getting into the intrigues of sales.