Has the toolmaker specified how the brass blank is held, including the adapter and fittings behind the fingers? I'd want that assembly against the installed door through removal and empty return, not another line showing the wrist can visit the fixture.
Include the human work around the machine too. Where does the setter stand, bring the fixture through and service it with the proposed base in place? Those tasks can be obstructed even if the robot's own route looks comfortable.
That gives the layout review something concrete. A changed base position could affect the robot path and loading again, so I would have the integrator compare complete alternatives with the setter, not relocate the base on the strength of a trolley outline alone.