firstly everything is possible.

second:
"What I would really like is some method that would give me the correct y value... without having to invert or choose between y or -y (I THINK IT'S IMPOSSIBLE)" ---> if you do that means you break ecdsa. You trying solve problem that pubkey is in d<n/2 or d> n/2

third -> you can check how many times is fliped (y) (as 02 to 03 and 03 to 02) depends on subgroup during adding point . but it is not possoble, you can't check   n/2 subgrups -> hundreds years.. you know ... or you are immortal:D