Those are good suggestions, Inedible.
Even though I'm a long time meditator, sleep can still be an issue for me too. If it's not caused by lack of sleep, it can be seen as a form of resistance. Another way to deal with it is to just be aware that the body is moving into sleep and turn your attention to the awareness itself. Sometimes that works for me.
Whatever the cause, it will pass as everything eventually does. It's best to observe whatever comes up, without reacting to it.
As far as the difference between sleep and deep meditation, the brain waves might be the same, and if it's deep enough (sleep or meditation) the ego will not be active or identified with. But with deep meditation, pure awareness will be there whereas in sleep it won't be. There might be some background thoughts, but it'll be like small, background static in the vastness of your awareness...a cosmic consciousness
Hmm, I hope that makes sense....
Bhavya