We do not really understand the climate well enough to tell how well we could compensate. However I checked the Wikipedia on Ice Ages and it seems there are quite a lot of things vaguely associated with starting and ending of Ice Ages. This would give us quite a lot of things to try and while it would require a detailed simulation to give a "maybe" level answer of if it would be enough, every little bit would help. And the disasters associated with the abrupt change in climate would probably have reduced the amount of people to support anyway...
The obvious. Changes in carbon dioxide levels have been strongly associated with the starts and ends of Ice Ages and we already have and use the necessary technology on massive scale. And we have lots of carbon reserves even with current economics, with everybody motivated to not go extinct we could extract sea bottom methane clathrates and methane currently impractical to even properly study. And burning as much hydrocarbons as we can would give as lots of cheap energy for mega projects. Although we could simply release methane into the atmosphere, if we have no need for the energy.
These have an effect on sea ice in the Arctic and the Greenland glacier. Basically we'd want to increase the amount of warm water flowing in from the Atlantic. I have no idea how this circulation actually works, but it has been suggested the Bering Strait has an influence on this. We could either close it with a dam or make it deeper with small nuclear devices. Usually either would be insane, but desperate times...
Similarly the Panama and the Suez could be blasted open to adjust ocean currents, if simulations suggested that might help. Although even in desperate times these canals would probably be too valuable to mess with on the scale needed to make a difference. Maybe if models suggested the fall in sea level would make them unusable otherwise?
If you make the glaciers, mainly Greenland and Antarctica, darker by seeding them with large amounts of smallish black objects, they will absorb more heat. And manufacturing and spreading the "grit" gives a good excuse to burn lots of hydrocarbons. Benefit this has is that the polar regions are generally the most effective place to increase heat as the starting temperatures are lower.
Sahara, Arabia, Kalahari, and Atacama get plenty of sunlight. And then they uselessly radiate it into space. In the real world this makes people wonder about large scale solar power. With global Ice Age threatening people would be thinking about collecting the heat and using it to warm the planet. It is possible, although ridiculously expensive, to build huge networks of heat pipes connecting these deserts with nearby seas. Then you just fill the deserts with radiators that connect to the heat pipes when the temperature is high enough. Although the scale, and hence the cost, is astronomical, this has two advantages. It is simple, potentially zero moving parts and relatively cheap materials, so the maintenance costs once it has been built might be tolerable. More importantly it can be adjusted as needed in real time, which is a good feature to have, if you are meddling with the global climate on a massive scale. Which in this scenario we would be doing, anyway.
While we can't really do anything about these, it is good to remember orbital effects other than the distance have a significant, if little understood, effect on global temperatures. Since we are, in theory, currently in the middle of an ice age and the change of orbits would almost certainly also mess up these cycles, it is possible there would be some warming effects from the change.