I can sympathize with you, Larry. About 15 years ago I trapped and relocated 8 gray squirrels, and was not bothered by too many of those. But now, I'm inundated with them, and they won't go into the traps. I can defeat most of the red squirrels (the eastern cousin of the chickaree) with baffles, but it doesn't work with the grays. Don't spend a lot of money on a "squirrel proof" feeder, since they eventually manage to figure them out. I'm looking at one right now eating from my expensive "squirrel proof" feeder.
It worked for many years, until one finally managed to figure it out. Relocation is the only option I know of that's foolproof, but to be safe I'd take them even farther away than a couple of miles.
Maybe you could train a cat to only eat squirrels, and not birds?
By the way, which chickadees do you get at your feeders? I'm thinking that you could get Chestnut-backed, Black-capped, or Mountain, or maybe all 3 at various time of the year.