Wrong, when Jack was being flung back in time, he should have encountered his past self as he was being flung forwards through time.
The two grab hands, spin around, and are thrown back where they just were. Past and future Jack both fight their respective past and future Akus, killing them at the same time finally.
The time vortex closes, with future Jack truly remembering all the optimism he once had as he sees his past self (Also he should still have the beard at this point), while past Jack sees what he could have become and the dangers of dedicating yourself to only fighting.
Vortex closes, the day is saved, there are now two timelines. One where past Jack is a hero in the past and gets with that girl he made friends with when he was a child, and one where future Jack is a hero and gets with Ashi.
And also has an orgy with a hundred thick Scottish girls, because he deserved it after all the shit he went through.