the question actually brings up an even greater/broader Question: Is the 'By the Formula/Numbers Pro Bike Fit going to provide a 'Better' Position for either performance or comfort (or both) ??? than 'trial and error' ??? or a combo of both ???

but back to your Q
the page you reference has a lot of holes, but no matter, let's consider your choices.

1. let's assume the goniometer measurement actually means something, and high level performance riders fall in the 140 to 155 deg range. If you set to 140, what advantages does this give you?
2. Counter that, what does 125 give you?

If, in fact, whatever your hamstring flexibility, it's only one important consideration. But let's say your Hammies are your limiting factor in leg extension. If you go much further, what happens? Your pedal stroke becomes a toe down 'digging' style, which greatly restricts your power at the lower end of the pedal stroke. Your hips rock on the saddle further causing not only power issues but also comfort problems. Too much extension and the pelvis has to remain very upright to allow that extension. Upright hip means you'll have a harder time getting into a more aero torso position - which further exacerbates your power and comfort. A high saddle position also means you have to move forward with the saddle, which means further adaptation with the bars... and more importantly makes it difficult to get good engagement of the gluts without good reworking of position.

So really, any 'formula' is gonna give a rider with flexibility limitations a hard fit. That's why formulas are just 'start' placement; then you gotta work it to the individual.

My recomendations
take the leg extension info, your goniometer reading as acknowledgement that you can improve flexibility - as a target for improvment.

set the saddle height for yourself, as high as you can:
a. in conjunction with a saddle fore/aft which gets good torso balance and allows you to have as much pelvis angle as the legs/hip/nback will allow - at this point I don;t think you could overdo plevic tilt angle - so max it out.
b. your foot angle at the bottom of the pedal stroke is the same as the foot angle of the forward female rider (in yellow/orange) in the pic of the website you link to above. It may seem parallet to the ground, but it's actually just ever so slighty toe down...
c. your hips don;t rock while pedaling.
d. your feet are connectign with the pedals as 'flat' as possible, which also takes into account cleat rotation.

Then work on your flexibility - not just hamstrings, but overall, leg/hip/back and overall torso if you can...
and over extended time - months, slowly raise seat height as your flexibility increases. Riding is about using the assets you have at the time you're actually in the saddle, not what you hope to have, down the road.