We pursue further our work on (Born Reciprocal) Non-inertial Relativity theory. Starting with a brief review of the theory, and how Non-inertial Relativity redefines the notion of mass, the phase space particle trajectories in $ D = 2 + 2 $ are revisited by emphasizing the key difference between a truly $U(1,1)$-invariant mass $ {cal M }$ and the Lorentz-invariant mass $m$. The derivation of the generalization of the special relativistic expression of $ E = m ( 1 - v^2 )^{ - 1/2} $ ($c=1$) to the non-inertial relativistic case follows. This, in turn, leads to the non-inertial relativistic extension of Milgrom's modified Newtonian dynamics (MOND) law. In the most general setting, one finds proper-time $ m ( tau ) $, and spacetime-dependent $ m ( x^mu)$ masses for point particles, when the proper force $ F $ depends on $ tau$ or $ x^mu$, respectively. By recurring to the tools of Finsler geometry, we finalize by writing the generalized gravitational field equations in curved phase space in the presence of matter sources, like particles and cosmic strings. As a result, both spacetime and momentum space are curved. We conclude with some remarks as to why curved momentum space should play an important role in quantum gravity.