Having 1.5V Vpp ripple on a 3.3V supply rail seems more like an issue with the regulator / bulk capacitance than a decoupling capacitor, I would think?
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.
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).
Some small switching regulators go into a low power mode when the output current goes below a threshold. The frequency drops to some "hovering just above zero" level. I've had to artificially load a power supply, to get it to be stable, e.g., with a shunt resistor. Naturally, that's inefficient, so it goes onto the TODO list to improve the design.