I've actually discoverd this on accident, but i lost my notes on the math theory on how i arrived at it.
I came to the same conclusion, but not quite as simple
I wanted to compose in MIDI in 12/8, but with the "four" feel, because it's easier to work in triplets w/12/8 in MIDI
So somehow, and i forget how I did it, I multiplied the 4/4 tempo (say 40 bmps) times 3 - so 120 bpms, then i divided it in by 2 , so 60 bpms in 12/8 = 40 bpms in 4/4
which is really the same thing as you're saying.
THIS IS THE ISSUE - how does one arrive at the conclusion as to WHY 12/8 is 1.5 times faster than 4/4 ?
I actually figured it out before, but i forgot now - really sad
Is it this maybe ?
12/4 is 3 times as LONG as 4/4, so 12/8 is 1.5 shorter than 4/4??