That's an interesting experiment you did.
It proved something, but maybe not the useable rule intended because it's an apples and oranges thing. It proved that less tension means less required travel... but that's mostly observable when comparing two tensions
on one string gauge. So, on one given gauge, we can say less tension means less travel.
Good, but there are a few issues. First, this phenomenon doesn't much enter into the situation here of trying to time pulls. I know you weren't suggesting this, but we don't get to take one gauge and twist the tuning key to change it's pitch to achieve the better travel length or syncing we're after

The pitch we're shooting for is fixed. Therefore, if we're going to take the less-traveled route and try to time pulls using different strings (rather than a change at the bellcrank), only the gauge and it's associated tension can be swapped out. To change one is to change both, so two sides of the same coin.
I don't think we can draw a universal conclusion from the experiment that says "less tension means less travel." That may be true when comparing two tensions on one string where the core size isn't changing, but it is NOT true if we get to expand out and compare strings of different gauges, because the differing core size kicks in and complicates things as a whole new overriding variable. Put a thinner string up against a thicker string
pulling to the same pitch, and the thinner will always require more travel, even though it is under
less tension. I don't understand the metallurgy behind 'why,' but gauge matters more than does tension level in terms of how much distance is required to stretch it, say, a half-step up in pitch. That's why it's good to focus on string gauge rather than the tension calculator when messing with strings to time pulls. Really, don't mess with strings. Bellcrank changes are where it's at...