Dear Stargaze
I used to ride like you, in a sort of time trial position on a road bike, with forward saddle offset, and a long stem. I would have loved to buy that long road-time-trial hybrid handlebar - brilliant. This style of riding allows you got get down low and spin the pedals behind you, and go along very quickly.
However, the problem for me was that I was almost only using my thigh muscles to push push the pedals around. This meant that after a while (about ten years in my case) my core (butt) muscles became weak. And as my core muscles became weak, they could not keep my knees straight, which made my knees hurt after cycling, and did not strengthen my back either.
So I did two things
1) Core exercises. I particularly recommend exercises that improve rotational strength because the up down (squat like) strength is provided by cycling. Clamshells and reverse clamshells are the standard exercises for improving rotational strenght. I devised a standing version which I highly recommend (though I don't think anyone is doing it!)
2) I moved my saddle back a long way, and changed to a push forwards / pull back style of pedaling such as was popular (especially among the French, but also Lance Armstrong) in the past.
This means
2.1) I am no longer stomping with my weight, so I am never putting my weight into attempting to extend my crank arms, so it is easier on my knees.
2.2) Cycling now exercises my core (butt, back) muscles, providing the strength to keep my knees straight and pain free.
Tim