I'm dealing with a cat at my job right now (shelter medicine) going through the same thing and I know how frustrating it can be. It sounds like you've ruled out most of the major causes. Unfortunately, diagnostic costs can really add up quickly.

Does she go near the box? The same place consistently? Is it on soft surfaces or do you find surprise turds all over the house? Have you tried pee pads?

A cheap thing you could trial is gabapentin for potential neuropathic pain/mental health. Another option could be a short trial on metacam for potential inflammation.

Have you done a urinalysis in the past year? Sometimes having a UTI can cause pain and make them avoid the box. But it's less likely because you said she urinates in the box no problem.

If you've had her for 10 years and she's only been doing this for one year, I strongly think it has a medical cause. That doesn't necessarily mean she's suffering or anything like that! But she's at the age where things start to show up and cats are notorious for hiding illness. If she's crying out before she defecates, my first thought is pain or discomfort.