-chromium-dev +chromium-discuss
I don't think WebView support overriding the TrustManager either. Also, yes, reflection speculating on the internal architecture of framework components / non public API sounds a pretty bad idea. It might work on a particular version of Android, but it might break on some others or on other devices.
It might not be exactly what you are looking for, but what about achieving something very similar to certificate pinning on the app-side with webview.getCertificate()?
Unfortunately the version of WebView in 4.4 doesn't seem to support public key pinning (HPKP) which probably would have been the best solution for what you are looking for.