Thank you all for your thoughtful and helpful replies. First, I should have mentioned that I'm not using manual focus as I almost always do because the subjects (basketball size limestone sculptures--70+ of them--are almost at ground level, and my old and damaged knees don't want to get up and down that many times. I can't see the rear screen well enough while standing to focus manually. But the problem seems to be solved---I set the camera to back button focus so it doesn't hunt when I trip the shutter, and I open the aperture to 5.6, as suggested. Works perfectly! I will certainly get the latest firmware--I'm one version behind. It does amaze me, however, that my 645z, which is older technology, and much much slower to autofocus, isn't challenged at all by these almost monochromatic subjects photographed in shade, while the newish Sony has problems.
Thanks again for your help--hugely appreciated.
David Ward