I would expect partner to run from any X of 3NT. I will be irritated if partner passes the decision around to me but I will run. BTW I could easily have a ♣ less and make the 3♣ call.
In my TOX response structure 2♥ is a little bid of an underbid and 2♠ showed xtras and is invitational so I would accept with 4♠ altho I have no real problem with 3NT either.
You need a clearly defined bidding structure for you responses to a TOX and for the rebids by the TOX hand. To play a 1♥ rebid by the TOX hand as 17+ strikes me as counterproductive as nonjump responses to a TOX have the widest spread of values. It is probably better to allow it to be slightly stronger than a minimal opener.
I pass because partner had multiple choices of calls over 1♥. viz 2♦, 2♠, 3♠, besides the call he chose. So yeah he has extra values but not enough extras for me to look for game with my hand
I would have to see the data and I am uninclined to search BBO. Plus I can only speak from my perspective. Pearson count is only the initial guide before I make a decision. A bad Pearson count and very short ♥ is a bad start if you are deciding to open.
It is a guide!!!(In my experience it works fairly well) you not only have to look at your ♠ but how short are your ♥ without either major you are close to playing 3m if you open :( and is not clearly your side's hand.
given the auction so far partner does not have a 4 card biddable ♠ suit, does not have 4♥, So is it significantly more probable that he has 3♠ than 3♥? If you believe so; take your last probable positive score and pass.
1] either 2♠ or 4♠ with a pref for 4♠ 2]no I think a 3♦ rebid instead of 2NT then over 3♥ I would call 3NT 3] with partner having wasted ♥ values (for a ♠ game) sell out for 4♠