You might take a photo of the poster and put it into a PPT because the students might not be able to see it.

You might assign a couple of students to ask questions after the presentation.

You might limit the number of presentations to 1 or 2 per day.

From my own experience, if you can frame the presentation as a riddle, students are more likely to pay attention because they need to figure out the answer.

Sometimes the newness of an activity can intimidate students. You'll have to desensitize the students to presenting.

If I do something like you did with my students the first time I do it has to be extremely guided. So after they make their posters I walk them through writing down what they're going to say (Step A: "I want to be world president." B: "As your president I will... because..." Step C: "I will also ... and ... because...") and then how they're going to say it; students know that if they want to change things they can, so if someone is more advanced and wants to write/say something else they will. Then they hold a partner/group practice. And then they present.

Since boys are normally more vocal in my classes they're partnered with girls (to make things easier my seating arrangement is girl-boy) with the qualifier that both have to speak.

There are 2 ways I'd run the actual presentation. The first way would be a speed-dating Round-Robin format. The 2nd is the traditional soap-box method (my kids have a sense of humour so I might actually have them stand on a soapbox of some sort). And since this is about being president, I'd have them secretly vote for their best poster/presentation: a lot of students won't want everyone to know who they're voting for so a secret ballot will take away that pressure.

If there are certain criteria you're looking for in their presentations, have the students score the presentations on their ballots (so the voting sheet will have a mini-rubric & score chart).

The next time I do a similar activity I'll make it slightly less guided because the students know what to expect, the time after slightly less guided, etc. etc. etc.