Making best use of server resources – memory & 404s

I look after https://www.oldies.org.uk/ – a website run by volunteers aimed at rehoming elderly rescue dogs. Each dog has a page written up by a volunteer, and when the dog is rehomed, we move it from the ‘Adopt an Oldie’ category to the ‘rehomed’ category. This was originally done so our volunteers could see that dogs were going home and feel they were achieving things, and it turned out to have the welcome side-effect that people searching for dogs often found one of our ‘rehomed’ pages and moved on to look at dogs still in need of homes.

The site has been running since 2005 and is fairly popular, and we’re now finding that we’re struggling for server resources and sometimes get out of memory errors. I’ve done the usual tweaks (caching with w3 total cache, cloudflare, an increased memory allowance, removing a couple of theme customisations that were running uncached queries), but it’s a small charity without much budget. Searches across 11,652 Posts are taxing our resources.

I could trim the older posts, but I’m concerned that if I do that, I will then get a pile of 404 traffic for those old posts, and I don’t think 404s can be cached either, so that will make the problem worse not better.

What can I do to make best use of our limited server resources so that users can still run searches and access other uncached content?

The page I need help with: [log in to see the link]