Welp...

Consider that they revealed Typhon Mount as the new Gold Saucer MGP sink in the Preliminary notes... I'm going to assume that the first hairstyle is going to be Shifting Canals.

Get your body ready for it.

"Should a portal appear when opening a treasure coffer found using a gazelleskin treasure map, it will lead to either the Lost Canals of Uznair or the Shifting Altars of Uznair. The destination will be chosen at random."

So RNG for portal, RNG for correct portal, RNG for wheel spin, RNG for item in chest, RNG for lot!

5 layer RNG, baby!