If its an irregular object, I doubt there's any easy way to estimate the submerged percentage, that method would be easiest with something displaying some kind of symmetry.

You could just poke it down with a pin or something. As long as the volume of the poky thing is negligible compared to the volume of the chunk of wood, it should have very little impact, plus it would give something to discuss in a conclusion.

Alternatively, weigh it down with weights of a known volume, then subtract the volume of the weights from the volume of displaced water and there you go. I would prefer that method to poking or estimating.