My understanding is that almost NO directional AM operating-as-designed will function as-is with HD. Tinkering is always required; the common point impedance curve is never suitably flat or linear. And many, if not most, directional systems can't be flattened and wide-banded sufficiently without a complete rebuild, which explains why very few AM stations operate with HD at night (note that a large proportion of AMs, particularly those dating to the 1945-65 period, run NDA daytimes and go directional at sunset.) So rather than spend potentially hundreds of thousands on antenna rebuilds which would require FCC licensing, even the few HD-AM fans out there are simply opting to turn off the Hissmaster at sundown.
My information is that adapting WMVP (former WCFL) 1000 Chicago for HD cost millions. And eventually it was turned off anyway.
There are of course exceptions, but many of them are high-powered AMs owned by companies whose people have invested heavily in HD, either financially or career-wise, frequently both. And many are 1A clears which are nondirectional anyway (although there are problem cases even with NDA 50kw'ers like KDKA.)