  Neutron stars provide a powerful probe of axion dark matter, especially in
higher frequency ranges where there remain fewer laboratory constraints.
Populations of neutron stars near the Galactic Centre have been proposed as a
means to place strong constraints on axion dark matter. One downside of this
approach is that there are very few direct observations of neutron stars in
this region, introducing uncertainties in the total number of neutron stars in
this ``invisible" population at the Galactic Centre, whose size must be
inferred through birth rate modelling. We suggest this number could also be
reduced due to stellar dynamics carrying stars away from the Galactic Centre
via large kick velocities at birth. We attempt to circumvent the uncertainty on
the Galactic Centre population size by modelling the axion signal from better
understood populations outside the Galactic Centre using {\tt PsrPopPy} which
is normalised against pulsar observations. We consider lower-frequency,
wider-angle searches for this signal via a range of instruments including
MeerKAT and SKA-low but find that the sensitivity is not competitive with
existing constraints. Finally, returning to the Galactic Centre, we compare
populations to single objects as targets for axion detection. Using the latest
modelling of axion-photon conversion in the Galactic Centre magnetar, we
conclude that within astrophysical uncertainties, the Galactic Centre
population and the magnetar could give comparable sensitivities to axion dark
matter, suggesting one should continue to search for both signals in future
surveys.
