There is no treatment, other than regular pruning as you performed to create the single trunk condition.
This is normal behavior for each of these species. As you keep the new suckering growth removed in favor of growth in the crown, these plants will make less investment in new stems from the base. It will never stop completely, but will be reduced in numbers in time.
Stressful conditions will increase the frequency of the suckering stems. Keep the plants well-watered and otherwise vigorous to reduce the likelihood of these new stems from the base.
I agree. One thing that might reduce the amount of suckering is if you twist off the suckers instead of cutting them to damage the growing point. I`ve also seen a plastic that was wrapped on the trunk which seemed to reduce the amount of suckering.