i may be mis reading this, but wouldn't you just select the 3 objects (top,middle, botom) that makes up that ledge and use "Combine" under Edit Polygon Tool to combine them? then merge the vertices you want to be together > delete unwanted edges > delete unwanted vertices > use "Split Polygon Tool" to add in edges to match the edges on the right image you posted.

That's what i would do, if i understood it right.