Does it make sense to fine-tune saddle forward-backward position without also adjusting the height?

Context

To reduce bum pain after switching from cycling shorts to winter clothing (base layer + cycling waterproof trousers, with no gel pads), from an otherwise just-about-right saddle position, I moved the saddle forward (on two occasions, by 2 mm each time). I chose forward because my sit bones were losing contact much of the time with the saddle. Now one ligament (the left) in one leg (the left) hurts after riding (pain level 2-3 out of 10). I’m trying to figure out a compromise.

Question

In the figure below, the point of contact of the dashed circle and the dashed line segment is the point where the sit bones touch the saddle.

Assume you have already figured a "just-about-right" adjustment of the saddle height and the saddle forward-backward position. Assume also you did not tilt the saddle. It remained parallel to the ground.

From that initial adjustment you can assume (?) that the distance of your pelvis from the cranks (large dashed circle) is about right.

Now, every time you decide to fine tune this (already about-right) adjustment by moving the saddle forward, you also need to adjust the height of the saddle, since otherwise you’d be changing the distance to the cranks, when you have already decided that that distance is already good.

Is this true?

Conclusion

If saddle height and fore-aft are not independent adjustments, the conclusion would be that the basic adjustment sequence (saddle height; saddle fore-aft; reach) is flawed. The sequence would be either:

• Repeat until there is no pain:
  1. Adjust height.
  2. Adjust fore-aft.
• Adjust reach.

Or, since fore-aft itself affects reach:

• Repeat until there is no pain:
  1. Adjust height.
  2. Adjust fore-aft.
  3. Adjust reach.