Okay, let’s take a simpler situation lacking relativistic speeds. Mass can be observed to be lost in its own reference frame, say, when deuterium-tritium fusion takes place. There’s a certain amount of mass beforehand, and measurably less after the fusion takes place. Thus, mass is not conserved. I expect you’ll have a tough time reconciling your theory with this.
Actually, not really. My theory also claims that mass and energy are different facets of the same thing (steam and ice). Any mechanical machination to inter convert them is fine with me.