Well, you dispelled the two thoughts I had. Seat adjustment and pedaling too slowly. If you are at 80-85, that shouldn't be slow enough to cause knee problems. A friend of mine used to climb hills all in her big ring, which meant a pretty slow cadence, even though she climbed pretty fast. Eventually she started complaining that her knees were bothering her, so she learned to make herself go into her small ring on steeper hills and spin faster.

She, however, was clipped in. And that could be part of your knee troubles. Is there a reason you don't clip in? Are you working toward that as a goal or do you never intend to? Your knees are working a lot harder than they would if you were engaging the pedal all the way around the stroke. So, it makes sense to me that this is your problem.

As for seat position, hopefully your expensive conversion resulted in the proper fit for you. If your seat is too low, it can cause problems on the top of the knee. If it's too high, you can have problems behind the knee (which I have experienced).

So, if you are sure the bike fit is fine, and you aren't pedaling super slow, my guess is the lack of clipless pedals.

As for getting faster, it's not always about being in a harder gear. Spinning faster in an easier gear makes you go faster as well. You'll figure it out as you go. Of course, it's probably harder to spin any faster than 85 without clipping in.