I feel your pain, Paula. I had to remove a dead dogwood a few years ago and I'm still encountering it's roots. Such a pain in the rear. Usually I take a saw to the offending root and do my best but I can't always get it all out so I have to plant elsewhere. The property has had several large trees and shrubs removed over time. the trees were dying or dead. the shrubs were old pink azaleas and I detested them. still every now and then I hit a root. I struggled finding a solution for you but the only way around your issue is perhaps nice big containers and plant the bed areas with annuals that won't grow huge root systems. I know this is not the way you'd like it to be but I'm stumped-pardon the pun!