Sebastian has had a look at egg buoyancy as well and offers us an eggsplanation (apologies to pun haters but JVG will love it)
https://www.dropbox.com/s/kvm8nskg402dl0w/Sebastian%E2%80%99s%20egg%20experiment.pdf
How difficult it is to explain these things, although you have got the ideas about density correct, one way of reading this might make the reader believe that the egg gets less dense rather than the water getting more dense, which we all know is the case. Proof reading is so important!
Keep them coming.
IRP