Ok, you can have the setup you have on the ground floor and not have to change anything - to place goza mats on stairs you need to stand on the spot where you want the goza mat to go, then double click it and target yourself. It should fall to your feet. Raise em up and no one will ever see the steps they cover.
To get rid of that anchor step, you have to put it in the path of another staircase. As you have already observed, when you erase a staircase clicking on any part of it, all of it vanishes. This holds true even if parts of it are missing - that is to say that a staircase takes up 4 tiles and each one of them is tied into the staircase:
X
X
X
O
The X's are where we have placed teleporter pads, and the O is what is leftover from the staircase (it is the bottom step) after we have deleted all of the other parts of the stairs. This means that the three X's are now "hotspots". If I was to place a staircase that had any part of it placed on the X spots and then erased the O spot, that would poof whatever was on the Xs:
AMMM
X
X
O
"A" is the bottom step of the newer staircase (AMMM) and as you know you can't just erase it, and teleporters don't work to get rid of it. By erasing "O" tho it will remove everything in it's path, including "A" and leave you with this:
XMMM
For a double L shaped staircase the easiest way to build it is to lay down the four teleporters in the corner, put down 2 staircases and hit floor trans twice, delete the four teleporters, then place the next 2 staircases, delete the original two staircases, then put down four teleporters and build the original two staircases again. Maybe doing that will help more than my letter diagrams, hehe