I'm by no means an expert, but are you comfortable in the position you're in now, and are just trying to alleviate the knee pain?

The way I've always done it is to put on all of my riding gear, click the shoes in to the pedals and adjust until my leg is fully extended(not locked or hyper extended). Traditionally, I think the norm is to adjust until your foot is parallel to the ground at the bottom of the pedal stroke. I'm always pretty fresh off the bike with that setup, minus my lagging muscles and willpower : )

Geometry scares me, so I'm not sure how the trig on that all works out, nor do I have any idea on where to chop the seat mast at.

Maybe see if you can get the overall stack height of the shoes, pedals, and saddle figured out on another bike, and then transfer that figure over to the seat mast bike? That should give you a rigid number relative to the center of the BB and the distance from the BB to the saddle top.

Also, depending on where your knee is hurting, you might want to keep it a little lower. From my experience, I get posterior knee pain when my seat isn't high enough. Alternately, it does reduce some of the quad fatigue that I get coming off the bike and into the run. Like anything in this sport, it's all about mitigating one pain in exchange for another...

Is your knee is an appropriate fore-aft position currently?

If yes, then you'll need to drop your seat and move it back.
If it's currently too far forward, you'll need to drop your seat a lot and move it back a lot.
If it's too far back, you may only need to move it forward.

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No trig masters out there?

SOHCAHTOA

It's not that there are no "trig masters," but that your question is not well posed, and the properly posed question is non trivial.

You'd need bottom bracket to seat tube axis distance, femur and tibia lengths, several measurements to relate the femur's upper joint to the sit bones, some ankle measurements... by the time you gather any of these measurements and calculate something you would have more uncertainty than you'd like.

If you approximate a bunch of things and just use an imaginary solid ankle and knee-to-sit-bone as the legs of a triangle, and assume no bottom bracket offset from your seat tube, you may be able to use law of cosines or similar, but you may "get what you pay for."

Not enough info to calculate using trig.

You didn't specify a length from the top of your femur to the pedal spindle, length of femur and tibia.

Knowing that you can use the law of cosines to figure out the rest if you assumed your foot angle remained the same in both positions.

There should be several cm of adjustment in the seatpost cap. Can you take a couple cm off the mast (not so much that you can't recreate your existing position) and see where it puts you?

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