I think this is a very difficult question to answer under any rules set, even in situations where we have arrived at the “endgame” where the life and death of all of the stones are not under question.
In another thread, I went down a wild tangent where I outlined some of the incredible complexity of evaluating the value of end game moves. I don’t fully understand it all, but I think it does involve calculation and symbolic reasoning that goes beyond mere numbers.
Dame are worth points under area scoring rules, but in most cases, at the very end of the game, the “true dame” should simply be split between the players, with one player getting an extra point if there were an odd number of “true dame”. Note, as soon as the game reaches a state where all that is left to do is fill an even number of “true dame” (ones that don’t require teire moves), then both players can safely pass (leaving an even number of true dame unfilled).
It’s important to clarify between “true dame” (for lack of a better term, maybe “strategically unimportant dame” or “dame that do not require teire moves” would be more descriptive, but wordy) and dame that do require teire moves.
In your specific example, playing at A is worth points for both players, even under Japanese rules. If white takes A, black will eventually have to reinforce at E3 (costing black one point of territory). Hence, it is not an example of what I’m calling a “true dame”.
These are very misleading statements and seem to reflect a misconception that the basic strategy of the game is significantly changed between area and territory scoring. Except if some very rare situations arise, players should basically play the same way regardless of the rules.
As for counting living stones on the board in area scoring, one can really think of it as a proxy for counting captured stones, or vice verse, since it is only the difference between the two players’ scores that matter.
In essence, there is no real difference (except for very rare cases) between thinking under area scoring or territory scoring. Note: under Japanese rules, one is technically compelled to fill all playable dame in order to avoid losing points.