So, the question I have for the OP is this:
I'm a player who likes to take my time with things, and be thorough. Now, when this new system was explained to me, I took it as an analogue for the adventuring day, so, every time I DO accrue 100 points, I rest, because I feel like that's supposed to be in line with the rhythm of time progression that's being simulated here... so as I explore and fight, I rest relatively often.
Now, we're in a video game, so the actual space I have to play with, and its contents, are limited, even if they make an attempt not to seem so.
The trouble is, I'm now at a situation where I have explored everything I can reach at the moment, and achieved all of the non-combat points that I have available without tackling a boss fight - I have boss fights in three directions, but I need to do at least one of them to progress at this point... Except, I don't have enough points for a rest right now, and my party is partially worn down and light on resources. I cannot beat any of the boss fights in my current condition. I also cannot rest.
What do I do, to prevent my game from being completely broken, and needing to restart it? Your system seems to allow for a broken game situation; how does it avoid that?