To jump back a few steps, I'd think that APGW could be falsified at least three ways.
1) From a top-down perspective, if warming over years & decades consistently decouples from models, then clearly the models are wrong. It's invalid to expect the models to be accurate month-by-month, that's not the granularity they are built to explore.
2) From a bottom-up perspective, if someone can establish on a theoretical basis that additional carbon dioxide & methane do not have a baseline or secondary warming effect, then we'd need a new theory to explain observations
3) If we see the regular surprise emergence of unexpected climate effects to the point where our models are invalid. I can't come up with a good example. Something like "Ocean water gets dramatically lighter above XX degrees, which vastly reduces the absorbtion of sunlight"
Do the models you are referencing account for magnetic fields & Birkeland currents?
During Grand Solar Minimums, the Solar Background Magnetic Field & Magnetic Field strength of sunspots is reduced, weakening both the Heliosphere & Magnetosphere, both of which repel cosmic rays, which trigger clouds, earthquakes, & volcanic eruptions. See the work of Dr. Valentina Zharkova, Dr. Heinrich Svensmark, & others (https://www.sciencedirect.com/science/article/abs/pii/S13429... ) for more details.
Earth is also going through a Geomagnetic excursion of the poles, which is geologically rare.