I’ve no idea how to stop the suckering, and my following warning is not specifically for ‘you,’ but don’t spray them.

Last year I removed a once beautiful ‘flowing cherry’ tree for an older woman who’d complained that it was dying… She also described having sprayed it’s ‘root suckers’ for years. As the herbicide feeds back into the trees root system – it will eventually kill the tree. I’ve also seen this ‘happen’ to commercially care for trees

Mow em, snip em, pluck em or dig them to graft ‘real trees to,’ just don’t ‘spray them.’ As mentioned, you surely know better – but apparently other’s don’t