Have you tried using the Surface Slicer View - that has the ability to use a HAL and create "Sliced Cross Section Samples of the Point Cloud (you can define the width of the sample parallel to the sliced Cross Section. In that view you can Select / Delete, Draw lines in the Surface Slicer View e.g. you can draw a "Cross Section" (use the Polyline command not linestring to snap into the plane of the cutting plane). You can set your step interval to be e.g. 5' or 10' and your plane width to be 0.1' or 5'whatever and then you can see a Cross Section Sample and manipulate it accordingly - I use this all the time to clean up Road or alignment based (e.g. Trenches etc) Point Cloud Data and I think it will do what you want.
The enclosed Video may help - there have been some additions since this video was captured that allow you now to create many cross section locations and make it easier to step through the cutting planes - but the concepts are similar - in this video I don't show how to edit the point clouds, but e.g. Polygon Select will work in Cutting Plane View and you can add point cloud selections to a Point Cloud Region etc from here
Alan