just one final precisation, #9 @statmatt
> The definitions of 'move' and 'turn' vary from person to person and site to site
Well it varies from game to game as well.
While OP was using the correct terms throughout (he mentioned 301. turn), my misunderstanding of what you meant was also from the fact that in your message you wrote "Games of Go 13x13 don't normally take longer than 84 moves each", and from that sentence alone, it was the incorrect next step to think of "move" to mean "go move" rather than "move as statmatt interprets it". Had I reflected on the number I would've instantly seen how the number was too low. Maybe i am just starting to think like a LLM, ouch.
But yeah. Chess-orientated or Chess-first websites such as this ones, use a different meaning: Chess goes 1. e4 e5 2. Nf3 Nc6 while Go goes 1 D16 2 Q4 3 D4 4 Q16 ... (of course, it is not written down like that, it is just for comparison) so all first player/black moves will be odd numbers, all white moves will be even numbers.
The way go moves are actually written down with pen and paper may be also interesting for some: the note-taking can be done on a sheet of paper (kifu) where you draw the grid you are using, and you place 1 2 3 etc on the intersections. That is a compact way to write down your game, if hard-to-read at first - it only uses one sheet of paper tops, even if the game goes on for hundreds of moves!
If chess were to adopt something analogous, that could be writing arrows to show the evolution of the board state - like one can see in those analysis videos, but that would become rapidly impractical (an arrow hell, a bit like in the memes)!