I did have a go putting my saddle up 5mm, I got scared and put it back after though.
This was on the trainer, the feel was quite pronounced, interestingly my average cadence dropped from 91 rpm to 85 rpm, the stroke felt stronger, but knee wasn't 100% happy still. So said to me it needed to go higher still.
Feels like I'm in the realms of being limited at both ends due to injuries, shorter cranks should bring both ends closer to each other, so should end up happier. CBA spending the money though.
Bear in mind you might just need to get used to it, knee pain after first ride out might not mean much.
My knee started sore this morning but all it took was a mental cue to pedal properly (see point someone made above about learning to pedal again). For me, the cue is not to push the pedals up and down (which brings in the quad) but to focus on pushing forward with the hip when the foot is coming over, like you're opening up the hip rather than pushing down on the pedal.
Starting to now get knee pain/feeling loss of control at the top of stroke, a strong argument for trying a bit higher now, right?
Perhaps keep it there a while first if pain isn't too bad, go easy and see if it settles - I think it takes a lot of hours to get used to something in a way that you know it's not causing issues or you're able to isolate things. You can move these things along too fast but it's hard to change things too slowly.
All in all sounds like shorter cranks would be money well spent?
