There are different kinds of roads in Ecuador. Are all of the airports served directly by the interprovincial highways you mention? If the roads to get in and out of the airport are city or local jurisdiction roads, then the interprovincial highways strike won't affect them, it'll only affect which route you can take once you get out of the airport.
So you need to look into which kinds of highways they're striking against, and don't assume that it's all of them. Then once you figure out which kind of highways aren't affected, you may be able to plot alternate routes, even if they're not nearly as efficient as the interprovincial highway route.
Plus you need to figure out when and for how long these events that shut down certain highways are happening. (Just random pictures meant to scare you don't provide enough information.) In most places, strike actions don't happen 24/7, they happen at certain times of day (they may be timed for the biggest effect, for example, such as during peak driving times if it's a highway workers strike). So if you can just wait it out, that might be another option.