Thanks @QWp6t , I already stumbled upon this, but it’s only for webpack-dev-server: “This plugin has no effect when webpack program is used instead of webpack-dev-server.”. Unfortunately Sage uses BrowserSync as its server, so it’s not applicable here as I understand it.
Edit: Ok, so my hack above stopped working a few days ago for no apparent reason. After a lot of struggles, I finally tried the WriteFileWebpackPlugin. Works like a charm! (with a few hacks, see in Github below). Turns out I misunderstood how Sage watch mode works. It’s using browsersync-webpack-plugin (different from browser-sync-webpack-plugin!), which internally actually uses webpack-dev-server, so my idea above was false. Phew, that’s a pretty hard first time with Webpack for me 
Thanks again.
More info in this Github issue comment