I understand your concerns at this time and will address them as you presented them...
Yes, geriatric osteoarthritis is most likely.
Purring also indicates discomfort in cats.
Vetergesic (buprenoprhine) is a potent opiate and would be expected to provide up to 12 hours of analgesia. In cats, however, behavioral effects aren't uncommon. They may include excessive purring, pacing, and rubbing. His becoming unsettled suggests an adverse effect to the opiate which shouldn't be continued.
If he has tolerated the prednisolone well - and his blood tests indicate that that's the case - I see no reason to discontinue that steroid. Meloxicam (Metacam) is an alternative but it isn't expected to provide additional antiinflammatory activity and/or analgesia than does the prednisolone. Please note that you mustn't give a steroid such as prednisolone concomitantly with a nonsteroidal antiinflammatory drug (NSAID) such as meloxicam. That's a ticket for gastrointestinal ulceration. In addition, the NSAIDs bring their own possible adverse effects; for instance, meloxicam can be worrisome when renal insufficiency exists as is assuredly the case in a 15 year old Bigglesworth.
In summary, medically speaking you're doing as much as I could ask of you. Please consider adding fish oil to Bigglesworth diet at a dose of 40 mg/kg daily of the EPA in the fish oil product you choose (a human generic is fine). The omega-3 fatty acids in fish oil are antiinflammatory. EPA is the most anti-inflammatory of the omega-3 fatty acids. In addition, consider either the over the counter Cosequin or prescription Dasequin available through his vet - neutraceuticals which might be of value and synergize safely with his prednisolone.
Please respond with further questions or concerns if you wish.
Thank you for your kind accept. I appreciate it. I can't set a follow-up in this venue so please return to our conversation - even after rating - with an update at your convenience.