One thing that may have to be taken into consideration when discussing
this problem is the displacement of water.  If the top and bottom of an
upright are sealed properly and no water enters the cavity, then you
have a funny shaped boat which displaces a certain amount of water.
That amount will also have to be taken into consideration.

I just remembered an episode of Northern Exposure (TV series) where
Chris, the disc jockey, catapults Maggie's upright Knabe (I believe)
into a lake.  If I remember the episode correctly, after about two
minutes to seeing this piano (or pianos) flying through the air and
being photographed from different directions, it actually lands in the
water, and I believe after a short period of time resurfaces to float.

Of course this is the land of TV and not reality.  I would imagine that
if anyone has connections with that show, they would be able to verify
if the piano did float, or what they did do in the experimental stage
of producing that episode.  Have fun in your research! :)

Mike Walter