How to feed suet to GS Woodpeckers, but not squirrels?

My garden backs onto woods so naturally we have a lot of birds but with this comes a lot of squirrels. There are so many and they are such a problem here that I have to feed all of the food from squirrel proof feeders. My question is, does anyone have any ideas for how I can feed suet to the GS Woodpeckers without feeding the squirrels? I have a fat ball feeder with a cage around it but obviously this keeps woodpeckers out. I did try using a squirrel peanut buster feeder with suet pellets in it, however I’ve found that these just get stuck in the feeder where birds can’t reach them and they go mouldy. Any ideas would be appreciated. 


Many thanks