  Implementing Poincar\'e's `geometric conventionalism' a scalar
Lorentz-covariant gravity model is obtained based on gravitationally modified
Lorentz transformations (or GMLT). The modification essentially consists of an
appropriate space-time and momentum-energy scaling ("normalization") relative
to a nondynamical flat background geometry according to an isotropic,
nonsingular gravitational `affecting' function Phi(r). Elimination of the
gravitationally `unaffected' S_0 perspective by local composition of space-time
GMLT recovers the local Minkowskian metric and thus preserves the invariance of
the locally observed velocity of light. The associated energy-momentum GMLT
provides a covariant Hamiltonian description for test particles and photons
which, in a static gravitational field configuration, endorses the four `basic'
experiments for testing General Relativity Theory: gravitational i) deflection
of light, ii) precession of perihelia, iii) delay of radar echo, iv) shift of
spectral lines. The model recovers the Lagrangian of the Lorentz-Poincar\'e
gravity model by Torgny Sj\"odin and integrates elements of the precursor
gravitational theories, with spatially Variable Speed of Light (VSL) by
Einstein and Abraham, and gravitationally variable mass by Nordstr\"om.
