For the record, I'm considering making the time limit optional, a choice you make at the start of the game (alongside a different one that I will reveal later). It would break the game and its intended purpose, but for players who absolutely cannot stand a time limit of any kind, at least they'll have a choice. The ending is going to lose a lot of its impact on them, but I can warn them about this when they make the choice in the first place.
I personally feel like choosing to remove the time limit would be like pissing in your pants to stay warm, but if it's the thing that decides whether or not someone even plays the game, to begin with, then maybe the proverbial pissing of your pants should be an optional feature after all.