Note that I went through all the standard steps of disabling all plugins other than Event Tickets, and Event Tickets Plus. And then there was no slow-down.
I re-added plugins individually until I found the conflict.
The conflict is with Easy Digital Downloads https://easydigitaldownloads.com/. As soon as I enabled that plugin, with Events Tickets, the problems returned.
When I have all other plugins enabled, including Event Tickets, but not Easy Digital Download, there is no site problem. But as soon as I also enable Easy Digital Downloads, the problems return.
I cannot disable Easy Digital Downloads as this is a core plugin that we use on our site, for controlling digital downloads.