I think the most important thing is to not conflate weather and climate. Weather is a local, relatively instantaneous, open system whereas climate is global, long-term and less open.

Weather is chaotic in part because energy can be rapidly brought into or removed from a weather system like a storm (a storm can go from over ocean to over land, or encounter hot and wet or cold and dry air, or the incoming solar radiation can change because of sunrise/sunsets), because internal circulation and lateral boundary conditions are really important (Navier-Stokes) and because water phase transitions (freezing/melting, evaporation/precip/sublimation) are all rapid and can account for a big chunk of the available energy.

The earth's climate is a bit different. Incoming energy from the sun doesn't change that rapidly--the sun has some 'weather' patterns and then there are earth's own orbital patterns that very regularly over periods from 23,000 to 100,000 years (Milankovitch cycles). But these are changes of a few % over long term. Very different than a hurricane hitting land or afternoon sun causing microscale convective systems to intiate. Greenhouse gases can change the amount of energy lost to either direct reflection of incoming short-wavelength solar radiation or later, long-wavelength radiation (i.e. radiation of energy that was initially absorbed rather than straight reflected), and again these changes are a few % net. Additionally, the earth's climate can't interact with any other climates, unlike weather systems.

There are some other things to keep in mind particularly about ice ages, ice sheets and changing greenhouse gas emissions. First, the timescales are important. Unlike some chaotic math functions, the changes to the global ice balance is mediated by the processes involved. Melting of ice sheets can happen as quickly as the ice can absorb heat--this is relatively fast. However, continental ice sheets don't grow by freezing of liquid water (we're talking Antarctica/Greenland/ the Laurentide ice sheet that covered northern North America, not the Arctic seasonal sea ice which is minuscule in comparison and can't cover land). Continental ice sheets grow by slow accumulation of snow. So this takes a lot of time relative to melting (tens of thousands of years).

>The massive increase in carbon dioxide into the system is an impulse that seems to have moved the attractor in a scary direction. Why wouldn't a massive impulse in the opposite direction do the same?

Because we're still moving in the same direction by reducing emissions, just less rapidly. We'd be changing the sign of the second derivative, not the first, much less the root function (CO2 through time). A good way to think about it is a big pot of water over a heat source. The climate is the broad distribution of heat in the system, the major convection cells, etc. The weather is the eddies and other turbulence. What we're doing by modifying greenhouse gases is changing how much the lid on top of the pot is covering the pot. Slowing emissions is more or less just covering the pot more slowly. Now, there are feedbacks in the climate system (more clouds mean more reflection of solar radiation, etc.) but in general we're still adding insulation to the system which is really unlikely to cause major, long-term cooling.

What worries me is direct, large-scale climate engineering: doing things to block incident solar radiation, etc. rather than reducing greenhouse gas emissions (this also won't help ocean acidification and other major ecological issues). I think the possibility of unforeseen consequences is much, much higher than going back to emissions levels that have been observed recently. Like Ol' Dirty Bastard said, "let's take it back to seventy-nine".