Best way to make a float stay afloat?

How about a bag full of table tennis balls?

I forgot to mention we’re on a pretty tight budget.

empty milk cartons?

Used truck tire tubes. Ask for them for free at the gas station.

You can always attach more wood at the base of the plywood sheet. In fact, you only need enough flotation to keep the plywood out of the water (so that it doesn’t disintegrate over time) when it’s weighed down with fowl. The closer to the water, the better, in fact, because it will be helpful if occasional wave action can help to clear it of the guano that will build up over time. I’d even suggest drilling holes in the plywood (small ones that webbed feet won’t penetrate) both to reduce weight and aid drainage.

A couple of logs like you’d put under a raft?

You can use water bottles:
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