There are no rifled first strike barrels available for the Phantom.
For that matter, I'm not aware of any rifled first strike barrels available for anything besides the Tiberius guns.
That said, I've played several scenario games using First Strike rounds in my Phantom and I've always just used my stock barrel. It's bored for .687-.688 which seems to be just about perfect for FS rounds and all the other Phantom barrels I've got are considerably tighter.
Therefore, my advice would be to just use the stock barrel and breech load them as you're planning. That's always worked for me, especially since the Phantom's barrel unthreads so quickly and after taking your first strike shot you can instantly re-cock the gun and start feeding your normal paintballs again.
The only trick is finding paintballs that are the same size as FS rounds, otherwise you'll run into problems with rollouts and/or velocity differences between the two types of ammo. Valken Crusade has been a good match in my experience, also boring out around .688