I might be more aggressive and remove all the 20 foot runners. Removing only 1/3 will be safer and will not sucker as much as if you take them all out, however, the 2/3 you leave will grow A LOT after you cut the other ones. Also this process will take a lot longer. I guess it depends on how much of the total tree these runners are. If you are only removing 20% of the total foliage you are probably OK taking them all out. If it's much more than that, I'd only take some out each year.
You may get a bunch of suckers for several years you will have to prune out, but your tree will look better quicker. The big thing is to only cut those runners if they are less then 1/3 the diameter of the branch/trunk they are attached to. If they are thicker than that, they may have to stay or be reduced until the trunk/branch they are attached to grows so they are only 1/3 as thick.