  We consider an MSSM extension with anomaly mediation as the source of
supersymmetry-breaking, and a U(1) symmetry which solves the tachyonic slepton
problem, and introduces both the see-saw mechanism for neutrino masses, and the
Higgs mu-term. We compare its spectra with those from so-called minimal anomaly
mediated supersymmetry breaking. We find a Standard Model-like Higgs of mass
125 GeV with a gravitino mass of 140 TeV and tan(beta)=16. However, the muon
anomalous magnetic moment is 3 sigma away from the experimental value.
  The model naturally produces a period of hybrid inflation, which can exit to
a false vacuum characterised by large Higgs vevs, reaching the true ground
state after a period of thermal inflation. The scalar spectral index is reduced
to approximately 0.975, and the correct abundance of neutralino dark matter can
be produced by decays of thermally-produced gravitinos, provided the gravitino
mass (and hence the Higgs mass) is high. Naturally light cosmic strings are
produced, satisfying bounds from the Cosmic Microwave Background. The
complementary pulsar timing and cosmic ray bounds require that strings decay
primarily via loops into gravitational waves. Unless the loops are extremely
small, the next generation pulsar timing array will rule out or detect the
string-derived gravitational radiation background in this model.
