Our work here is done
Well, would you look at that—while we were sleeping, some kind programmer elves cobbled together some shoes for us! The Transform.rotation page of the Script Reference has a chunk of code that "smoothly tilts a transform towards a target rotation". That sounds a lot like what we're trying to do.
Hey, I have an idea: I'll keep an eye on the door. You copy and paste this code into your game. If anyone asks, tell them "the book made me do it".
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