How often do you do oysters? One time a week should provide the zinc you need. BUT, if you're not absorbing well enough, or getting *too much* copper, zinc deficiency is totally possible.
Its really hard, from what I've read, to absorb the zinc from nuts/seeds, so I might not *count* those as great zinc sources...
If you really want to avoid supping, I might try taking digestive enzymes along w/ a serving of oysters once a week. It will help you to absorb the zinc.
I personally feel supping, at least while your getting your levels up, is only helpful, but we each need to do what works for us.