This entire “glitch” is posited on the idea that altering your subjective past does not alter your absolute present.

And you’re right - that’s ridiculous. Why wouldn’t taking away something from the past alter the present? This is called causality and thermodynamics, and it’s one of the reasons physics, as we understand it presently, doesn’t really allow for time travel as it is popularly conceived. It’s not about gold coins, exactly, but the idea that you can’t end up with more energy than you started out with (or the mass equivalent of energy).

But OP started with the idea that a time machine which break causality and thermodymnamics exists, so I just pointed out how massively broken such a machine would be.