  In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY),
which have been suggested to be the most likely version of SUSY to emerge from
the string landscape, higgsinos are expected at the few hundred GeV scale
whilst electroweak gauginos inhabit the TeV scale. For TeV-scale heavy neutral
SUSY Higgs bosons H and A, as currently required by LHC searches, then the
dominant decay modes of H, A are into gaugino plus higgsino provided these
decays are kinematically open. The light higgsinos decay to soft particles so
are largely invisible whilst the gauginos decay to W, Z or h plus missing
transverse energy (MET). Thus, we examine the viability of H,A-> W+MET, Z+MET
and h+MET signatures at the high luminosity LHC (HL-LHC) in light of large
Standard Model (SM) backgrounds from (mainly) t\bar{t}, VV and Vh production
(where V=W, Z). We also examine whether these signal channels can be enhanced
over backgrounds by requiring the presence of an additional soft lepton from
the decays of the light higgsinos. We find significant regions in the vicinity
of m_A~ 1-2 TeV of the m_A vs. \tan\beta plane which can be probed at the high
luminosity LHC using these dominant signatures by HL-LHC at 5\sigma and at the
95% confidence level (CL).
