No, this doesn't work. Medomai the Ageless has an ability that says
Medomai the Ageless can't attack during extra turns.
It doesn't matter what caused you to take the extra turn in the first place. If you're in an extra turn, it can't attack.
Medomai simply cannot attack during extra turns, these don't have to be the turns given by him, but can be any extra turns. Medomai can give more than one extra turn, from having doublestrike or from multiple attack steps in the same turn, I do this very thing in my Rafiq of the Many EDH deck using Rafiq himself to get double strike and Finest Hour to get the extra attack step. Once the first of those extra turns you stack up with Medomai starts, the ability that prevents him from attacking kicks in until your next normal turn.