We do use lots of the super-calls from WebView.PrivateAccess, several of them are used from ContentViewCore through the InternalAccessDelegate interface. So, we can't just avoid solving this problem.

Out of the calls we make into WebView.super, the following are hidden (this is easy to test by creating your own class Foo overriding WebView, and copy-pasting WebView.PrivateAccess into that class, replacing WebView.super calls with Foo.super).

performAccessibilityActionInternal
setFrame
startActivityForResult
onDrawVerticalScrollBar

WebView.PrivateAccess.super_performAccessibilityAction calls WebView.super.performAccessibilityActionInternal.
WebView.PrivateAccess.super_performAccessibilityAction is called from WebViewChromium.performAccessibilityAction if mAwContents.supportsAccessibilityAction is false (otherwise we call mAwContents.performAccessibilityAction). Currently AwContents.performAccessibilityAction always returns false, but there is a TODO from dmazzoni there to implement that method in WebContentsAccessibility.

setFrame is only called directly from WebView.setFrame:
WebView.setFrame -> WebViewProvider.ViewDelegate.setFrame -> WebViewChromium.setFrame -> WebView.PrivateAccess.super_setFrame -> WebView.super.setFrame
this is a bit ugly, but I don't think there's anything we can do about this for existing Android versions - for P+ we could just have WebView.setFrame directly call WebView.super.setFrame.

WebViewChromium.InternalAccessAdapter.super_startActivityForResult actually falls back to using reflection to call WebView.startActivityForResult for Android versions before N (exclusive). Note that this works because WebView itself doesn't override startActivityForResult to call into the WebView APK (that would cause an inf loop).
So, as long as we never implement startActivityForResult in the WebView class, we could use reflection here.

onDrawVerticalScrollBar is called in a similar way to setFrame, calling from WebView, through the WebViewProvider.ViewDelegate.

It looks like we could use a Java class called MethodHandle to invoke a super class method:
https://docs.oracle.com/javase/7/docs/api/java/lang/invoke/MethodHandle.html

MethodHandle handle = MethodHandles.lookup().findSpecial(clazz, methodName, MethodType, callingClass);
handle.invoke(supportLibraryWebView);

I'll try this to ensure it works.

And it turns out MethodHandle was added in API level 26 :/

There's more I think. Eg onDetachedFromWindowInternal calls super as well (though not from glue or chromium code)

Darn, ye you're right, it's just not called from WebView.PrivateAccess (which is where I've been looking)

This is not an issue atm since we use none of the super calls.