I would say there’s two parts to this; the contact point measurements (bar height and position, distance to saddle, seat tube angle, position relative to BB etc) which would be relevant for your knee and back pain issue.
The second part would be the overall geometry which may well be more difficult to copy onto other bikes, especially if you are comparing ht to fs, the static vs weighted / active geo can be quite different.
Having said that, it’s easy enough to measure up the bike you like and try out changes on your other bikes to test and see if you like it.