Ok, your Pico would have had the weaker diode in it if it was from the KickStarter, but looking at the voltage you're fine so that won't be the issue. It looks like the internal RC oscillator is just way off.
Looking at the source code it's possible I could add something that allowed you to tweak it for a different speed RTC. I don't know if that's something that would help at all?
I've just had a go at it but something isn't working right I'm afraid. I need to look into it in a bit more detail.
I think realistically fitting the Abracon ABS06-107 is the best way to get decent accuracy though - even tweaking the RTC won't bring it to the same kind of levels you'd get from a proper crystal.
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