Wall cleanup issue

Am trying to cleanup the intersections of my various interior partitions such that the intersection lines/ not in a plan view of these shapes will communicate appropriately the boundaries of the wall types at the various wall intersections.  I understand that the connect forms tool is the correct way to perform this task but it does not work as expected.  Am attaching an image file which describes what I am expecting to be able to do.  This is a very basic exercise that so far has taken way way longer than is reasonable to expect and I fear that it might not even be achievable in BA.  Or perhaps I'm using an outdated tool and should instead be relying on a different command for this task?  Any guidance would be appreciated.