I'd say it starts with dialing back the "new feature/change fetish" that a lot of web developers have. Yes, I know some things simply can't be done without a JS webapp, but not all and probably not even a majority, so if HTML and CSS will do the job fine, then so be it; and even if it needs to use JS, it likely doesn't need to be latest-browser-only JS either.
The constant "X is bad, use Y; no, Y is bad, use Z; no, Z is bad, use..." churn and that "push the web forward" trendchasing seems to be so entrenched in "modern" (there's another buzzword) web dev culture that I wonder if Google/Chrome is responsible for cultivating and propagating it, because it's not quite as endemic in other areas of software and also helps Chrome keep its monopoly, since it keeps the target moving and beckons at others to "catch up".
I think web developers need to adopt a more "do what you can with what you have"/demoscene-ish (for lack of a better term) attitude and not the silly "I could do it with just X, but I'll use Y because it's newer/better-but-I-can't-explain-why-and-everyone-else-is" that really just assists Google's monopoly. In other words: Writing a webapp that could work over 20 years of browsers may not be as hard as it sounds (I've done it --- and I'm not even a web developer --- which might be the reason why...), and you will definitely help browser diversity that way.