  We examine production and decay of heavy neutral SUSY Higgs bosons pp-> H,\ A
-> \tau\bar{\tau} within the hMSSM and compare against a perhaps more plausible
natural supersymmetry scenario dubbed m_h^{125}({\rm nat}) which allows for a
natural explanation for m_{weak}\simeq m_{W,Z,h}\sim 100 GeV while maintaining
m_h\simeq 125 GeV. We evaluate signal against various Standard Model
backgrounds from \gamma ,Z ->\tau\bar{\tau}, t\bar{t} and vector boson pair
production VV. We combine the transverse mass method for back-to-back (BtB)
taus along with the ditau mass peak m_{\tau\tau} method for acollinear taus as
our signal channels. This technique ultimately gives a boost to the signal
significance over the standard technique of using just the BtB signal channel.
We evaluate both the 95% CL exclusion and 5\sigma discovery reach in the m_A
vs. \tan\beta plane for present LHC with 139 fb^{-1}, Run 3 with 300 fb^{-1}
and high luminosity LHC (HL-LHC) with 3000 fb^{-1} of integrated luminosity.
For \tan\beta =10, the exclusion limits range up to m_A\sim 1, 1.1 and 1.4 TeV,
respectively. These may be compared to the range of m_A values gleaned from a
statistical analysis of the string landscape wherein m_A can range up to ~8
TeV.
