The notches won't be fixed. The notches occur when the phase shift is n*180 degrees where n = 1, 3, 5... Each stage contributes 90 degrees of shift at the critical frequency. Even if some stages are fixed all the notches will move because the overall phase shift is changing. Modulating a subset reduces the depth of the sweep. With 10 stages you're getting a lot of sweep so you don't need to modulate every stage. Modulating a subset also reduces the cost and the sensitivity to VCR mismatch.
Also, that schematic on the web has errors so...
I'd guess you can get pretty close with a 10th order phaser.
I could add a parameter that selects the number of stage to modulate but I don't think it's necessary, simply reduce the sweep depth.