This (IME) depends on how the netlister and ERC respond to
duplicate ports.
One thing that has worked when multiple same-named ports
are shorted for cause (by design) and the tool complains,
is to take the port labels off all but one (replace w/ plain
text, for documentation purposes).
But check the ERC settings, you may be able to suppress
shorts warnings (which, if thrown on features which are
obviously the same net and the same port name, means
the tool is not getting it) either globally or specifically
Another option, if the tool comprehends resistance and
does so using a marker polygon, is to impose trivial-L /
trivial-R regions between the pad and the plane, and
name the GND pads to (say) GND1, GND2, GND3... and
let the netlist think the milliohms are on purpose (if you
care about simulation, make the schematic represent
the real pad-plane L, R). You might have to alter how
you lay out the pads (like, relieve the corners and make
current flow orthogonally outward from the pad only on
the three sides, through three resistor-polygons in parallel,
represented to suit).