Finally found the cause of the slow searches for both photos and cemeteries. We felt it was related to some update from last spring -- probably in March -- but we had not been able to locate the problem. An update today to the search software fixed the issue. We hope that the fix will not introduce any new errors (and usually they do not).
Fixing this is a relief as it was very frustrating for both the users of the website *and* the website developer.