Simon, just completed a program designed by Physio, in conjunction with sports injury surgeon, to be completed at gym to overcome same issue. Took me about 4 months, but wasn't chasing the muscle strength thing too hard, so limited sessions to about 1 hour four times a week.
Like you I was avoiding surgery. Did mine would you believe a strong frog kick to swing a race sail up and out of the water

Physio indicated this swim technique is one of the worst for knees and this injury, particularly if over 50 years of age.
Ex AFL footballer was my physio, so his knowledge of this issue is right up to date.
Yes same here with brace, had to use it for about four weeks before any attempt at a rehab program.
Program was a success when I went for a knee strength compatibility test, where there is less than 10% difference in pull and push between both knees.
So if you can, get to a sports injury group so they can assist you.
Mineral