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I am not familiar with the Variable Mass Hypothesis and you may be right that this cosmology explains the redshifts of deep space objects better than the standard model. That bar isn't all that high but I can't imagine that such a theory could overcome the Big Bang in the foreseeable future because the BB can always be patched with another dark horse explanation or ad-hoc assumption.

Personally I would welcome more Machian view of cosmology. One such view that I know of is based on the Sciama effect which is essentially Einstein's gravitational frame dragging in reverse. With frame dragging the motion of a massive body can accelerate the motion of a nearby object but, with the Sciama effect, the total mass of the universe is considered to be inertially at rest and any objects in motion relative to the mean rest frame of the universe experience a cosmic drag on their velocities. This is contrary to Newton's law where objects in motion remain in motion. This cosmology explains distant redshifts as a Sciama related drag on light so it is a version of the 'tired light' theory. Since this theory and Narlikar et al's VM hypothesis both depend on the total mass of the universe, they may be complementary.

Which theory of gravity are you using? As I understand it Mach considered gravity to work instantly so every massive body in the universe was instantly and directly connected to every other massive body. Mach explained that when a train stops suddenly the passengers fall forward because their attachment to the distant stars is greater than their attachment to the train so inertia was a matter of environment and dependent upon the total mass of the universe.
Einstein considered non-local action (spukhafte Fernwirkung) to be impossible because one massive body could not communicate its gravitational attraction to other massive bodies any faster than c. This view makes inertia a local property of matter itself and not dependent upon the mass of the universe. Einstein explained gravity as curved spacetime but Mach considered Einstein's absolute space to be too metaphysical to serve as an explanation for gravity since we can only speculate about space by observing the matter within. Mach preferred explanations based only upon what we can directly observe rather those based on things we can not observe like empty space.

Check your BAUT PM.