I had terrible problems with sparrows eating the chicken feed too (you can read all about my battles on "My Coop" page). I designed and made a couple treadle feeders and they immediately ended the problem of wild birds eating the feed. You can find plans on how to build one in my signature line. A cheaper and quicker alternative to the treadle feeder is a trigger feeder. People seem to be very pleased with them and you can read about them here. Finally, if your coop is relatively wren-resistant with the exception of the pop door, you could put up vinyl strips over the pop door to keep them out and put the feed inside the coops. Vinyl strips like these are relatively inexpensive and would keep wild birds out while letting your chickens to pass through. There would be some training with each of these methods, but any one of them would help reduce feed loss.
Hmmmmm........DH has seemed bored of late, perhaps I should do him a favor and slip your treadle feeder plans in his lunchbox in the next few days................I mean, I'm just thinking of him because I know how much he enjoys a good building project (especially if it's for my chickens).