It's very simple. The Majority Leader, in discussions over the UC, simply tells the Minority Leader: "fine, you have the right to debate the subject on the floor." If they don't, then they vote. It's that simple. Really.
So they all sit on their thumbs. They don't have to talk, and they don't have to agree to vote. Cloture is there as a substitute for UC when there are a handful of dinks.
The way I see it, the objectors don't have to vote, and they don't have to talk.
I admit I don't have solid citations to the UC "rules," other than the general citation to all of the Senate rules. Can you walk through how the rules are applied to obtain the scenario you outlined?