I have adjusted everything on my bike over time, possibly 30 or 40 times over for each thing.
Saddle, stem, seatpost height, bar angle, everything. And it's now just perfect.
The reason I mention it, is because I am absolutely riddled with arthritis all my life, and if I can get comfortable on a bike, anyone can.
No need for medical intervention atall and I didn't have to pay someone £300 or £400 plus.
If you have a serious ongoing knee problem, no amount of physio or bike fits will cure it. I think it's probably more about striking a balance, not spending a fortune on a bike fit by a medically trained person.
You said yourself that the frame wasn't made for you, so I just think it's good money after bad.
It seems to me aswell that the service you are seeking is something akin to pro cycling. But I fear that even something like that wouldn't help you to the degree that you may expect. What with ongoing knee problems.