I was just thinking about "minimum effective dose." It really depends on the stage you are at in your journey and your personal situation.
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As you say:
"I'm hoping the small daily fluctuations while reducing more closely mimic natural daily cortisol fluctuations so we can sneak past the body's patrol system."
Yes.. assuming the problem is only adrenal insufficiency
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However ... as you say:
"No need to roll out the alarm response, business as usual."

This assumes the beast of PMR is no longer a threat. If PMR is still a threat, you may need a "fight or flight" response to a potential flare. Consider taking more Prednisone since you won't get much help from your adrenals.
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Another possibility is the beast of PMR is only stalking you. Your stress level is still high but PMR isn't an immediate threat. In that case ... it is hard to know what to do!

All to say ... there is no minimum effective dose. It just depends on your situation at the time. It can be a combination of many things that dictate what Prednisone dose you need. Your HPA axis won't be very helpful with adjusting your cortisol level according to your need.