[jeffreyH (OP)]

Will the Planck minimum action vary with choice of coordinates?

[Mike Gale]

I think not. Photons demonstrably lose energy as they climb out of a gravitational field and the energy loss correlates exactly with hf.

[jeffreyH (OP)]

I am surprised anyone replied to this. When analysed properly the idea is rubbish. I sometimes wonder why I post such nonsense.

[Mike Gale]

There are no stupid questions. Variable h crossed my mind at one time, too. It was when I first learned of variable light speed in Schwarzschild coordinates and variable G in MOND theory. The reason why h can't be observer dependent is not immediately obvious.

[PmbPhy]

I am surprised anyone replied to this. When analysed properly the idea is rubbish. I sometimes wonder why I post such nonsense.

In this case you're right. The question is meaningless. The Plank's constant has units of action. That's about it.