Yes, I’m guessing it will all have to be part of a local situation that has to be either left as-is or played out in full (if you tenuki partway through you suffer a loss). I think this could happen for a variety of tactical reasons (including but not limited to a semeai), but I really don’t have any idea coming close to a solution, hence this thread asking for help 
What would be even more desirable* is if we can find a position where the “sequence” for both players is just a single move. For instance, this corner in isolation has a swing of 7, miai value of 3.5, requiring only a single move from either player to make their gain:
*More desirable as a substitution for playing with the button rule, since it would be less likely to interfere with the game in other ways, such as providing ko threats. Although ko threats can maybe be worked around by making the chains involved big enough that sacrificing any of them can never be worth it for a gain in the main game.
Somehow such a single-move button seems even less likely than one involving a sequence of moves, at least on the regular board… but what if we allow other graphs?
On a 5*1 board we can at least get down to a swing value of 5, miai value of 2.5, with this position:
But I don’t see how to push this lower - seems like this is a pretty minimal space to setup a seki with odd number of dame (you need one eye in the seki, one spot where black will play to create the seki, and one dame).
So currently it seems more likely that it’s possible to find a longer sequence of moves with miai value of 0.5. (I’m assuming it is possible since Bill Spight wrote that he had done it!)
Edit: This position that I constructed some time back features a move with a 3-point swing value, by getting around the need for a black eye. However, it’s a super delicate setup and relies on the superko rule and the global board state. (it would lose its special properties if considered together with another board where white could make a group with 3 eyes). And even ignoring all that the 3-point swing is still too big!