Turns out that you actually can save in these levels, but you have to do it manually from the pause menu. You can get unstuck that way by saving and then reloading
Finished Notch's level yesterday, and saved all crew members in Souleye's first level. My main problem with that level is too many points of no return that you can't know about until it's too late, which means you miss out on trinkets. I ended up with thirteen or fourteen out of a possible eighteen. There's some great new music though.
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A hare like me couldn't catch up to Black Turtle.