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.
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"
This is why the term "climate change" is more accurate than "global warming". Increased energy in the atmosphere has uneven effects. The overall effect is to warm the earth but due to second-order effects (changes in cloud cover, changes in precipitation), some places won't experience warming but will experience change.