Draw the line by account instead of by geography, since both parties legitimately cover the same map. Workable splits are named accounts served direct with everything else through the partner, a revenue threshold above which accounts go direct, or an application split where technically complex work goes direct and standard product goes through the channel. Publish the choice to both reps and partners, write an explicit deal-registration rule covering credit and expiry, and give the direct rep partial credit on partner-sourced business in their territory so they do not compete with your own channel.