OK, I give up.
I will continue to use Microsoft Entourage as my main email client. I can find no reasonable way to move out of Entourage / Hotmail to Gmail. Or anything else.
One of the many reasons I hate Microsoft is their kind of proprietary, closed, anti-user behaviour.
DEATH TO MICROSOFT.
Still, my preferred email is RickMcCharles AT gmail.com
Rick McCharles 
Thunderbird for mac no good?
Still, I have no way to forward my new hotmail messages into any mail clients other than those made by Microsoft.
Years ago I could, but not more.