Sometimes in highly called areas a little different sound can be effective. I've had good luck switching to a bird distress sound in the Midwest at least. The woodpecker is probably second to the rabbit in most used, but it still seems to work. Especially in tighter quarters where volume can be kept down a bit. For mouth calls a higher pitched call has been best for me. I've probably called in more with the various versions of Verminators tweety call than all others combined. A lot of this is because it's what I start out with. For more volume their alienator call can hit the high pitches too, and both can do an excellent bird distress sound.
When calling alone I often switch to the electronic call, a FoxPro prairie blaster II in my case. I love my mouth calls but it's easier to get high percentage shots and not get busted when the sound is not coming from right where I sit. I'm a believer in decoys to take the attention off me too. Calling with other people I use the mouth calls and hide in more cover, set them up to shoot.
Decoys need not be fancy but need to get high enough off the ground to be visible. The Mojo critter is one I use a lot with the extension and I've had a coyote pounce on it before. The one built into the FoxPro works good too but is only about 15" off the ground. When going light and covering a lot of distance on foot I carry one I built from a snap clip, fishing line + swivel, tape, and pheasant tail feathers. I taped them together in an X and tied the fishing line to it. The swivel keeps the line from twisting and I hook the snap clip to a limb. It spins dances around like crazy with a little breeze and has been effective. Biggest thing on a decoy or electronic call is not to bet busted setting them out. Sometimes it's better not to use them if you can't sneak them in effectively.