Betelgeuse to nova ? Not a hope - so don't hold your breaths for it happening anytime soon !

There is one small flaw in your argument. If the 15% reduction in a star's diameter is due to gravitational collapse when the supply of hydrogen at the core is exhausted, then the subsequent ignition of helium fusion should result in a massive INCREASE in size. That's because the temperature at the core of a star when helium fusion begins is FAR higher than it was for hydrogen fusion, and that heat radiates outwards, resulting in the outer layers of the star expanding to a considerable degree.

Betelgeuse is already a red supergiant, which means that it started fusing helium into carbon and oxygen a LONG time ago.