I've had helpful comments on "unbeknownst" from people in the US and UK who know such things, linguists, editors and so on. Henry Fuhrman, in charge of copy editing at the LA Times, tells me via Twitter (@hfuhrman) that the "-st" form is the commonest in their articles, if not the usual one. Other US correspondents confirm this.
Still seems curious (though not unusual, I have been told) that quite a rare dialect word should establish itself in standard, "quality press" AmE. Was it a 19C British and Irish dialect form which caught on there more strongly than here? Comments from Scottish and Irish contributors on Lynne Murphy's (@Lynneguist on Twitter) excellent and comprehensive blog, which covered this, I find, several years ago, say that it has always been the usual colloquial form for them. And it seems to be established in the UK press now too.