Kabby
I suggest you check out Duncrafts web site. They carry some thing called a "squirrel buster" feeder. It has a forest green top and base with 6 feeding ports and a 15" tall by maybe a 3" wide clear tube to hold the seed. I have used one since 2009 and it is fantastic.
It has a round, weight sensitive feeder ring/perch at the base by the feeding ports. It comes 'factory set' for the weight of a Cardinal. Anything heavier then that, then internal sensor slides and closes the feeding ports. It is adjustable too!
Red wings, Starlings, Blue Jays are all too heavy to land and feed. I think it would be perfect for your needs.
I employ 2 right now, one with "finch mix" and the other with black oil sunflower. They are fantastic because the little birds I have, Titmouse, chickadees, both Nuthatches, House finch and Goldfinch have easy access to seed.
I have one feeder filled with the cheapest seed I can find! I let the chubby birds feed there.
Other vendors may have it cheaper or whatever but that's what I use and I think it will solve your problem!!
Good luck!
