Hi Nate, thanks for the question,

Although there are some herbicides listed for control of suckers, It appears that Roundup for lawns (northern) is not listed for use on suckers and would most likely damage the tree. Growth regulators like "Sucker Punch" effectiveness may be questionable. Off label use of pesticides is illegal.  Those listed for the purpose may require multiple applications and must follow the specific label direction.  This should be left to orchard professionals.  Pruning back to the source such as the root is the suggested approach.  Note that sucker production could indicate the tree is in stress. Check out the following links:

Managing Suckers on Fruit, Ornamental, and Shade Trees | Yard and Garden (iastate.edu)

Can water sprouts and suckers be prevented on trees? | Extension (unh.edu)

Managing Suckers Around Fruit Trees | USU

I hope this is helpful.