RE 2., I doubt it'll help - for at least two reasons, already mentioned by 'duskwuff and 'daveguy.

RE 1., definitely worth trying, and there's more variants of such tricks specific to models. I'm out of date on OpenAI docs, but with Anthropic models, the docs suggest using XML notation to label and categorize most important parts of the input. This kind of soft structure seems to improve the results coming from Claude models; I imagine they specifically trained the model to recognize it.

See: https://docs.anthropic.com/en/docs/build-with-claude/prompt-...

In author's case, for Anthropic models, the final prompt could look like this:

  <role>You are a chess grandmaster.</role>
  <instructions>
  You will be given a partially completed game, contained in <game-log> tags.
  After seeing it, you should repeat the ENTIRE GAME and then give ONE new move
  Use standard algebraic notation, e.g. "e4" or "Rdf8" or "R1a3".
  ALWAYS repeat the entire representation of the game so far, putting it in <new-game-log> tags.
  Before giving the new game log, explain your reasoning inside <thinking> tag block.
  </instructions>
  
  <example>
    <request>
      <game-log>
        *** example game ***
      </game-log>
    </request>
    <reply>
      <thinking> *** some example explanation ***</thinking>
      <new-game-log> *** game log + next move *** </new-game-log>
    </reply>   
   
  </example>
  
  <game-log>
   *** the incomplete game goes here ***
  </game-log>