What I still haven't seen in is just 1 climate model that explains most of the observed current and historical data
The reality is that the world is too complex and weather too chaotic to come up with 1 model that you're going to be able to plug what we know of what happened in the weather into and get out a simulation that follows what actually happens. The proof of this is that weather forecasters are commonly completely wrong, and they're dealing with the best-quality records we've got (e.g. the extensive weather doppler radar network in the USA) and only have to make predictions about rainfall, temperature, and cloud coverage for a day or a week in advance.
Our maps are just barely up to the task of modeling global weather in the way that you want, where we get to make specific predictions. Our understanding of localized weather patterns is inadequate to the task. However, that still doesn't prevent us from being able to make broad, generalized predictions from what we know of physics. And given that what we do know broadly fits the global warming narrative which in turn agrees with what we know of physics, there's no particular reason to doubt the overall picture. The globe is warming, and we're doing things which physics says should warm it. There are natural mechanisms which will serve to bring the system back into balance, like for example spreading extent of sea ice, but these mechanisms have literally never had to clean up a mess like the one we've made and it's unclear whether we're going to make it through the reset process because we don't actually know what that looks like. We've perturbed the regular cycle that we could have expected to survive in a somewhat unpredictable way, but we can still make some predictions. Just as the world is not black-and-white in the way that denialists want it to be when they argue that it's colder where they are so there can't be global warming, our lack of complete certainty does not make us completely unable to make predictions. If it did, then we would never be able to do anything, because we often find that our understanding is superficial — yet our previous models still enabled us to make useful predictions.