But the larger creatures have more HP, and thus can survive longer...
More HP? Really now, drowning has nothing to do with how resistant you are to other effects. An elephant can take more hammers than a mosquito, But it WILL drown faster. And Immaterial creatures shouldn't be affected.
Have you ever seen a drowning mosquito? I've seen a number of times and they seem to die very fast if covered in water, because (as far as I know) they breathe through many small holes along their whole body, so they cannot 'keep their breath' and generally small creatures have faster metabolism, so I guess mosquitoes die really fast when drowning, even if they remain on the surface of water.
On the other hand an elephant (... though I have never seen a drowning one ;P ...) could probably at least try to swim (I don't know if elephants are able to swim, but they are at least able to cross rivers and shallow lakes), depending on the circumstances he might even be able to keep his trunk over water to breathe, and I'm pretty sure he would survive much longer than a mosquito. I'm not sure though if elephants density is close to waters, or higher... as far as I know it depends mostly on the bone mass (bones are the only part of the body with density notably higher than waters) and volume of lungs (as long as they are not filled with water they are the main body part that lowers the average density.
IMHO drowning speed is not related to size, but to how much a certain creatures is adjusted to swimming. Small creatures can be adjusted to swimming, or not, as well as big creatures might be adapted to swimming or not. The shape of limbs, the way a creature breathes, it's density and body structure, all are much more important than overall size IMHO.
So game-wise I guess
and immortal should be immune to drowning and nothing else. It keeps the rules simple and should work, and I guess the instant kill makes the most sense, because even if a creature is able to survive longer before drowning, if it is unable to swim (or fly) it would be also unable to attack in such circumstances.