One technique we've used with moderate success is to pass a clipboard around. People can jot down notes, or conversational ideas that are tangentially related or unrelated. Sometimes that provides a convenient way for someone else to say "hey, what's this thing you wrote down about?".

It also could let you list your three things to talk about in a breadth-first manner rather than talking about each one sequentially.

It probably sounds like a better idea than it is in practice; the clipboard gets stuck when holders get distracted, or people still refrain from bringing things up, or whatever. But you might try it out anyway!