It is likely that this cat is having some sort of nerve pain that only occurs when she moves a certain way.  I had the same problem with my pitbull Phil; he would scream when sleeping but when I would go to him and feel him everywhere he acted fine.  I took him to a neurologist who could not find any pain but did agree to an MRI.  Phil ended up with a malformed vertebra that was pinching his nerve only when his head was in a certain position and he needed spinal surgery.  He is fine now and I have a good relationship with the neurologist so he trusted my opinion but that dog did not show pain if you felt him or moved his neck around; only when he slept.

My point is that your cat could certainly be in chronic pain but act normally at the vet.  It is reasonable to give gabapentin 50 mg twice daily for a 2 week trial.  At our clinic we get this compounded into a tiny tab by Wedgewood Pharmacy and most cats take it very well.  If your cat has normal kidneys then she can safely take the NSAID Onsior once daily for 3 days.  I would try those things first because they are most likely to help nerve pain.  If still unsure then you can use the narcotic buprenorphine.  You can give it orally or there is a long-lasting sustained release injection that lasts 3-5 days which is what I use post-op even after a cat spay.

I can not diagnose this cat from a video alone so if needed get a second opinion but maybe your current vet could at least prescribe the gabapentin and Onsior for a trial.

Pam