It's true that this is a relatively large deficiency in practice: how strong would a player be if he played the middlegame at grandmaster strength but couldn't reliably mate with king and rook?
The authors overcame the practical problem by just punting to Stockfish in these few cases. However, I think it's clearly solvable with LLM methods too. Their model performs poorly because of an artifact in the training process where mate-in-one is valued as highly as mate-in- fifteen. Train another instance of the model purely on checkmate patterns - it can probably be done with many fewer parameters - and punt to that instead.
When we have a won position we want to progress and convert it to an actual win.
I think the operational definition I would use for progress is a prediction of how many more moves the game will last. A neural network can be used for that.