I am much more mathematically inclined than musically. I have essentially no musical ability or ear for sounds.
That being said, I think you are correct when you say that the tone should be equivalent for any dimension of blade if it is tensioned to the same STRESS (psi), not necessarily the same static load (lbs).
I am also not a saw expert, but I should be pretty darned good with blade manufacturing, metallurgy, and the related engineering.
One very well proven technique in the carcass-splitting saws (used in primary meat production plants) is a torque-limiting adjustment knob.
This effectively ensures that all blades are tensioned to the same level when used on a saw. (The splitter saws can only accommodate a particular length and width of blade). The operator puts a blade on, then turns the knob until it slips at a pre-set torque. The blade cannot be over-tensioned, and as long as the knob is turned until the knob slips, it won't be under tensioned.
The Delta-style spring preload indicator looks like a valid system as well. Obviously, adjustments need to be made based on blade thickness, width, and tooth profile for this to be 100% accurate. I include tooth profile because the back-to-gullet distance is different for different tooth counts and profiles.
The lever-cam systems generally rely on spring deflection, so they should be consistent for a given blade geometry. (either always good or always bad).
The flutter and thumb-finger methods aren't as "mathematical" in my view. That doesn't mean that someone with good feel, vision, or ear tone can't use them very successfully, only that I prefer something based more on the mechanics of materials.
My 2 cents,