You don’t actually have to extrude anything to cut on the table. I rarely do. It sometimes helps to simplify the tool path selection but in your case it doesn’t sound like it. One trick I’ve learned that seems to unify the whole drawing is 2 select all copy and paste then move the copy to where you can use it and delete the original. I’m not sure what all happens when you do that but it seems to make the whole drawing one unit