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Yea since writing this I think it has more to do with the regulator circuit. I plan to do a small rewrite and change the title to something like "When 3.3V isn't actually 3.3V" to more accurately reflect the situation. A decoupling cap would probably still help, but there were some mistakes made on the regulator circuit.

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Switching regulators (and even linear regulators!!) have maximum capacitance ratings.

Adding more capacitance could, in theory, further destabilize your regulator.

The overall tank circuit (the inductor + capacitor forming the bulk of the switching circuit) is incredibly fragile.

It's legend that some old switching designs stopped working as newer tantalum capacitors had less resistance, screwing with the stability of older switching designs. You kind of need to choose exactly the "expected" kind of capacitor (aluminum caps have more resistance, which increases stability of the feedback but slows down the feedback).

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