I think that it’s implicit that the volume of Godzilla would increase; we need to assume that the bounding layer has a degree of elasticity and that that the matter displaced by the flotation cavity will expand into that, reducing the net density.

Mighty Godzilla, with power untold

Rises through the waves; his powers unfold

Hidden muscles in clever design

Create a new chamber as they realign

Inflating his body, a titanic display

Defying the depths, he floats up and away

No long bound by the oceans’s might

Godzilla soars, a triumphant sight!

Yeah, it’s been pretty universal in the UK for at least the last couple of years. Not sure where this idea came from.