I think you're right; on reflection, that's exactly the sort of thing I would expect rational!Peverells to do, plus the stone appears about the right age to be set up by the Peverells. Based on the same reflection, I agree with your predictions and the probabilities you've given them. Quoting for posterity:

Harry is the Master of Death, in the sense of being the primary magical owner of all three Hallows - 75%.

HJPEV counts as Tom Riddle, to the point that on death, the Horcrux network will attempt to update based on him. - 60%.

And I'll just make this my prediction comment for this thread. (Previous prediction comment.)

The prophecy stone in Chapter 96 ("the tall stone worn as though from a thousand years of age, upon it a line within a circle within a triangle glowing ever so faintly silver") and/or its behavior will become plot-relevant. 95% Otherwise it’s a major unfired Chekhov’s Gun.

The wand Quirrell produced from a false tooth in Chapter 107 (the one that he then uses to cast Fiendfyre) is the brother to Harry’s wand. 90%

Riddle’s Horcrux 2.0 (the improved version that resembles the 'false' description, but before he integrated the Resurrection Stone) is actually a lost earlier version of the Horcrux spell; Riddle rediscovered it. 70%

Observations:

This whole segment from Chapter 108 reminds me strongly of having something to protect:

"And you," said Professor Quirrell, "have no right to speak of happiness either. Happiness is not what you hold precious above all. You decided that in the beginning, all the way back in the beginning of this year, when the Sorting Hat offered you Hufflepuff. Which I know about, because I received a similar offer and warning all those years ago, and I refused it just as you did. Beyond this there is little more to say, between Tom Riddles."