Improving this site’s performance

Piqued by Peter’s recent post on Core Web Vitals I decided to submit my own home page and a post to PageSpeed Insights. The results were not perfect, but perfectly satisfactory; 99, 98, etc. But there is a bigger problem behind the scenes. Any time I change anything at all on the site -- a new post, a minor edit, major upgrades -- it becomes unreachable for about 15 minutes. The log files tell me that the maximum time allowed, which is 4 minutes, is exceeded, often 2 or 3 times a minute. Then, suddenly, the problem resolves itself. I'm really not sure even how to start troubleshooting this, because each time I change something like cache details, the enforced time-out drives me nuts. One possibility is that there are just too many pages for Grav to handle, more than 4000 in total. Of those, ~2500 are the silly little posts I make to record the podcasts I have listened to. But honestly, why do I need to keep those data? Or at least, keep them online. It all started in May 2018, and I…