Thanks for the suggestion, John. There is nothing final in what follows, but I thought an update was in order.
I’ve put a few hours into this already today (adding to the hours over the past couple of days), keeping more meticulous step-by-step notes. I did make a fresh action to make sure it was working, turned it into a droplet, and made new Lr export presets. I made a copy of the droplet in question, dragged it to my desktop, and tried a few times dropping files onto it.
It’s hard for me to effectively summarize everything I’ve observed. I hope what follows is not perceived as an off-putting tangle.
One of the confusing observations is that when I run the action (and I speak here of one-at-a-time trials using the droplet on the desktop, using the action in Ps, or using a Lr export preset with the "after export"), I sometimes observe that the file dimensions in Lr (in the metadata panel) haven’t changed, even though in Ps and the finder the size is what I expected.
In one case (having dragged the file from the Finder to atop the droplet), when the action was finished I observed in the Finder (which still had the file in question selected) that the file size had changed as expected (e.g. from 70+MB to 2+MB), but the dimensions did not change (the action that flattened the file should also have changed its dimensions). When I selected another file above it in the Finder and reselected the file in question, the dimensions changed to what had been expected.
In one final test I did, I used one of today’s new Lr export presets on 10 files (the preset applies a droplet after export). In eight of the ten cases, the files showed the expected new dimensions in both Ps and the Finder, but in Lr the dimensions in the metadata panel remained unchanged. In the other two cases, Lr, Ps, and the Finder are consistent (i.e., showing the expected new file dimensions).
Having used the same Lr export preset with the same action on ten files at one time, and having observed these inconsistent results, it came to mind that there might be something about certain files that causes the unexpected behavior.