I don't think you fully appreciate that what you talk about are several different aspects of the climate system and they are true at the same time. Which one is the more salient factor at play depends on the time scale you look at.
> fossil-fuel-sourced CO2 and CH4 are steadily warming the planet
No climate scientist denies this. It is the trend happening since the industrial revolution. But say, if you have three months or three years of data, you are not gonna be able to fit a statistically robust trend. At best, you can do some Bayesian attribution of the likelihood that a climate event is attributable to the long-term climate change effect.
> Many of the supposed discoveries of periodic oscillations in the North Atlantic and the Pacific simply don't hold up over time, and as with ENSO, have zero predictive power over what phase/amplitude of the next 'period of the oscillation' will be.
You are jumping into conclusions too soon. The fact that a system has periodicity does not necessarily mean that it is perfectly deterministic. You may not be able to predict when the next El Niño is gonna happen, but you can say with confidence how many El Niño events you will likely see in a 100-year time span.
> These phenomena are likely mostly chaotic in nature
Again, being chaotic does not mean no predictability at all. The atmosphere and the ocean do follow the basic laws governing fluid dynamics. How much predictability you have very much depends on the spatial and temporal scale you are looking at. Being able to predict one event and being able to predict a statistical distribution or a power spectrum are two different things.
> fossil-fuel-sourced CO2 and CH4 are steadily warming the planet
No climate scientist denies this. It is the trend happening since the industrial revolution. But say, if you have three months or three years of data, you are not gonna be able to fit a statistically robust trend. At best, you can do some Bayesian attribution of the likelihood that a climate event is attributable to the long-term climate change effect.
> Many of the supposed discoveries of periodic oscillations in the North Atlantic and the Pacific simply don't hold up over time, and as with ENSO, have zero predictive power over what phase/amplitude of the next 'period of the oscillation' will be.
You are jumping into conclusions too soon. The fact that a system has periodicity does not necessarily mean that it is perfectly deterministic. You may not be able to predict when the next El Niño is gonna happen, but you can say with confidence how many El Niño events you will likely see in a 100-year time span.
> These phenomena are likely mostly chaotic in nature
Again, being chaotic does not mean no predictability at all. The atmosphere and the ocean do follow the basic laws governing fluid dynamics. How much predictability you have very much depends on the spatial and temporal scale you are looking at. Being able to predict one event and being able to predict a statistical distribution or a power spectrum are two different things.