How is scoring resolved if a snapback situation makes it disadvantageous for each player to play first?
If both players decline to move would all stones simply be counted as live?
The corner is not resolved and should be played out. And it appears advantageous for white to force a resolution.
If it is disadvantageous to either player to force resolution, you have seki. If that case, the stones are alive and any territory touched by both players is not counted.
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It depends on the ruleset.
Under Chinese or AGA rules, whenever there is a life/death dispute, you play it out. Anything that remains on the board after playing out, is alive. So, if nobody wants to play here once disputed, both groups are by definition alive [the only exception to this rule is the extremely rare “Moonshine Life”, which is considered dead by Chinese rules], and you get the stones points (Chinese rules use area scoring). The dame is a neutral point which counts for no player.
Under Japanese rules, life and death are determined for each group independently by means of hypothetical play with special rules. Simplifying a bit, a group is said to be alived if it cannot be captured, or if it is captured, the opponent cannot prevent the placing of a permanent stone in the locality of the group. That is the case here, so both groups are considered alive in seki under japanese rules if the situation is left as is.
Game-theoretical considerations for the specific Torazu Sanmoku position (and also, for example, the Lasker-Maas rules) would give 3 three points for the position, just like in the traditional Shuwa ruling of the Torazu Sanmoku. However, no official institution uses such rules.
So, strategically, under modern Japanese rules, white should take and get 2 points, otherwise he would end up with zero points. There is a Ko possibility hidden here, but both sides have to cooperate to start the Ko, so the one for whom the Ko is unfavorable would not start it, so there will be no Ko actually.
Under area scoring (Chinese rules), it will be zero points (locally) if black takes and both play correctly, and either zero points, or two points for black (if black has a lot of ko threats for example) if white takes. Since black has currently 3 points if nobody takes, black will never capture here, since both white capturing and nobody capturing are better for him. Since white is better capturing than leaving things as is, under area scoring white will also capture.
So, under both major rules currently in use, white should capture here at the end, and black should just wait for white to do so.
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This last conclusion, “players should do exactly the same regardless of rules”, always holds except for when very specific events kick in. These are:
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One has an option to create a Seki with either odd dame / different total of eyes of each color, or not to create it. This is extremely rare.
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Superko rules (basically nobody uses this: Even at AGA major tournaments, which are supposed to use situational Superko, people have been seen replaying triple Ko games instead of using Superko, probably because they do not know the AGA Superko rule)
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One side has a position where he does not need to defend, just because if the opponent plays, a Ko would arise and the player has more than enough Ko threats than the opponent (also rare, but Go Seigen was involved in a rule dispute twice because of this, and curiously, the authorities ruled against him both times, even though he faced different sides each time http://senseis.xmp.net/?RuleDisputesInvolvingGoSeigen).
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Positions like bent for in the corner, together with unremovable Ko threats (seki), at the same time. Very rare.
Number 3) creates a one point different in the score for such a position, which is also very rare. The reason is that modern Japanese rules force the player to defend anyway (there are no Ko threats in hypothetical play), so he has to give up a point of territory. Under area (chinese) rules however, this defensive move can be made at the end, when all the dames have been filled, with no penalty at all. Note that dame points count as Ko threats for the purposes of such a Ko, since the player that wins the Ko is trying to win it without having to defend.
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Thank you for your detailled and well-explained reply!