So wow, super cool thread! In Aus Sydney, these things are damn strange. My wife has one & I just played with it. It’s not using any “standard” modulation. pm3 can’t detect it as ay type standard tag, but the above post about copying the first 4 blocks of the raw dump, doing a bit flip, converting to hex and writing to a t55 did the trick! It seems to be a “pyramid” based system, but with some custom tweaks to screw people like us over 
Awesome job working out the tricks to get a t55 to talk the same language!
Can confirm that the fob from the gym here is NOT a t5577, its some funky chip that there seems to be no public docco for yet. Yay, puzzles to solve!