I'd give him a 10xp ability that allows him to make free actions after his initiative but not during the initiative of others (or in response to). Then give him Surge of Speed and the Edgemaster's core ability to simulate that second turn.
Actually, you shouldn't need to spend any xp on this. I had the same conundrum, given that my current campaign is in an arc where the players typically go from fighting one large boss to another, with no other combats in between. To keep the fights interesting, I created bosses who- in ways you mentioned- have more than two half actions in a round, and then I simply had them throw in Delay actions (Fantasy Craft, pg 219) between actions to simulate a 'multiple turns' effect.
Granted, I may be misreading how Delay works by allowing creatures to delay, take one action, delay, then take another all within the same initiative account, but I have yet to find an instance where that creates trouble in play, even accounting for the fact that I let the players do the same with Delay.
Hope that suggestion helps!