I'm throwing in the towel on this one.
It landed on top of my towel. Current status for me is that, on first booting Safari, the dozen Top Sites boxes appear immediately with the names underneath them but without graphical content. Graphics take 19 or 20 seconds to load. The links work without the graphics.
I no longer have oddball sites - just what I have chosen and locked in place - and the two unassigned boxes change properly according to where I've been. it's good enough for now, so I too will just wait until Apple sorts it out.
iMac (Retina 5K, 27", 2017), 3.4 GHz Intel Core i5, 8GB RAM, 2400 MHz DDR4
OS Mojave 10.14.6
Canon MX710 Printer
Epson Perfection V500 Photo Scanner
Time Machine on 1TB LaCie USB-C
Carbon Copy Clone on 500GB OWC Mercury OTG Pro