Turns out that it was apparently the WebView not having focus that was the issue.
I discovered that using the arrow keys to get focus on the textboxes caused them to work, so I theorised that there was an issue somewhere with something not having focus, most likely the WebView not having focus. Sure enough, adding the following line seemed to fix the problem:
webView.requestFocus(View.FOCUS_DOWN);
I’m still at a loss to explain exactly why the issue occurred in the first place – the textboxes should work whether they receive focus from being tapped upon or through being “arrowed” to – but at least I have a solution that appears to work.
Thanks for your input wf.