Building overviews did fix the lack of display problem. It only took a minute on a 9 gigapixel mosaic, so the tool must be smart enough to leverage the existing COG pyramids. That's a relief and one concern of mine put to rest (don't create duplicates).
I'd still like to locate the max raster property. It's not in Set Raster Properties or Set Mosaic Dataset Properties gp tools. The latter does have 'columns/rows_maximum_imagesize' and I tried various numbers from -1 to 1000 to 8000 to 100000 with each having no apparent effect. (The mosaic is ~12,000 x 12,000 px.)
On the troublshooting trail I also encountered the very interesting Some raster images created using the Create Mosaic Dataset tool are not displayed in ArcMap. That's not the problem here but I've definitely seen that before, and not that long ago. My cure previously was to delete and recreate the mosaic datasets. and....there it is, use ArcCatalog to get at the max raster setting. That and all the other properties can be set there, and faster and easier then using the Pro gp tool.