Need to feed, peel paper backing, cut and place foam from a reel. Different lengths and around radius corners.
Has anyone done anything like this?

Your application is similar to peeling and applying a label. You may want to contact some label applicator folks. If you don't have success there, contact a general-purpose automation builder like Apex Automation.

Probably too late to help, but might want to look up Accuplace in Plantation, FL. The company specializes in equipment for picking and placing adhesive-backed components. www.accuplace.com