Interesting question, Millertime
When I go to the pool tomorrow I'll try out your suggestion. I don't feel that I have any particular balance problems on the back, except of course that the legs tend to sink, which I think is inevitable. It is worth experimenting, though. Perhaps the head could go a little deeper. I might need an observer for this, as what one feels one is doing and what one actually is doing are often quite different.
A friendly lifeguard might be prepared to help.