It's again possible there is no objectively best way

I'm not sure I'm willing to grant that's impossible in principle. Presumably, you need to find some way of choosing your priors, and some time later you can check your calibration, and you can then evaluate the effectiveness of one method versus another.

If there's any way to determine whether you've won bets in a series, then it's possible to rank methods for choosing the correct bet. And that general principle can continue all the way down. And if there isn't any way of determining whether you've won, then I'd wonder if you're talking about anything at all (weird thought experiments aside).