Bloody stool in senior cat (11F) — food-related or something more serious?

One of my cats, Aislynn (F, 11), has had intermittent bloody stool since the beginning of the year.

Food changes & onset of symptoms: • January/February: I was making a bit more money and wanted healthier food for my cat, so I switched their wet food from Sheba (they’d been on Sheba for nearly half a year) to Tiki Cat — both cats did fine. • March: switched dry food from Purina Naturals Indoor Cat Chow to a Tiki Cat variety. We transitioned very slowly (2 weeks). Shortly after introducing the dry food, the bloody stool started. • first, we weren’t sure which cat was affected since they share a litter box, but we’ve since confirmed it’s almost certainly Aislynn.

Stool details:

• Usually looks normal and well-formed. Occasionally mushy, rarely diarrhea.
• Blood is always at the end of the stool, small coin-sized, mucusy, and not throughout the poop.
• Her anus always looks normal — clean, no irritation.

General health:

• No loss of appetite, always food- and treat-motivated.
• Energy levels and behavior are normal: sleeping, cuddling, playing with our other cat (Rorschach, M, 6).
• No weight loss or gain during this time. Confirmed this with the vet visits and periodic checks at home.

Vet visits & adjustments:

• April: after a month of symptoms, vet suggested Fortiflora. It helped temporarily, but blood still appeared on and off.
• May: vet recommended switching back to Purina Naturals (her lifelong diet). Transitioned back in June, with Fortiflora. This worked for a while, but occasional bloody stools persisted.
• June–July: stools looked normal, maybe only 1 or 2 bloody stools found.
• August: I was away for 3 weeks on a work trip. She had one bloody stool while I was gone, and I’ve found two more since returning (1.5 weeks ago).

Other notes:

• I’m fairly sure it’s Aislynn’s stool because she sometimes refuses to use the box if it’s not perfectly clean, so I’ll occasionally see hers outside of it. Rorschach never does this. I can confirm this further via the crayon test if needed.
• Diet since June has been only Purina Naturals dry kibble with water added — what she’s eaten most of her life.

My concerns:She’s had this issue for over 6 months now. While food changes and changes to my work habits (including working longer hours at home between May and July and my work trip) could explain it, I’m worried if there’s a chance there could be an underlying condition. She otherwise seems healthy and unaffected, but the recurrence of bloody stool makes me wonder if it’s more than just diet/stress. My vet said in our last visit it seems more stress related (food, work) so labs and stool samples likely are necessary, especially since the other cat seems unaffected too.

Questions:

• At what point should I push for further testing (e.g., bloodwork, stool sample, imaging)?
• Could this still just be stress or food-related, even after all this time?
• Should I wait a bit longer and monitor (e.g., until end of September), or is this concerning enough to schedule another vet visit sooner?

Any advice, similar experiences, or input on what to ask the vet next would be really appreciated. Thank you!