The bodygripper in a bucket can be really effective, but may not be a good choice around feeders. Deer can be curious and while not normally inclinded to see your bait as something to eat, you don't want a small deer sticking its head in the bucket out of curiousity.

I'd shut the feeders down for a while and then use the corn as your bait. Gang set so you can get several in one shot. If using footholds, you could use a dirt hole set, but use corn down the hole instead of a more traditional lure or bait. The deer may mess with your sets though. A bit of molasses, maple syrup, and honey makes for a decent coon lure/bait. Add a bit of anise oil and/or vanilla.