I too avoid silicones bc of the reasons you mention, and bc it can eventually lead to very brittle hair (bc moisture can't get in, as you say).
My Wylie tends toward a greasy coat much sooner than my others, so I know what you mean. He also has seasonal allergies and is prone to skin infections during the season. Does yours have allergies? If yes, that could be why you're seeing a greasy coat.
I would avoid oatmeal products - despite the myths about them, they actually can make hair/skin situations worse. Vet Derms advise against them. You may want to try a medicated shampoo. I recently found a new one for Wylie and I cannot BELIEVE how much less greasy his coat is and how much longer he stays clean. The one I got for him is sold out, but this is a similar one (and look at the price, so cheap!):
Amazon.com: SynergyLabs VF Clinical Care...