Not going to work without some doin'.
A Phantom speedgate has a much wider diameter than the PGP's tubes, so unless you were to cut apart the speedgate so that it allows the bolt to clear, it won't fit the back of the gun.
Fitting it to front would be a pain too, and you'd have to use little grub screws or something to lock it onto the gun. Plus, a forward-facing speedgate invites the possibility of taking a shot down your feedtube and smashing up all your paint into a giant mess. I know this from personal experience.
You might be able to get the phantom part to fit unmodified if you extended the back of the tube rearwards a ways with some PVC, but the pipe would still need to be shaped to clear the gun and it would be so long that you risk having trouble getting a ball to drop into the breech.
There's a reason people pay so much for the Palmer parts.
Enjoy your PGP, though! They're a lot of fun.
After my stock feedgate broke, I made a custom speedgate from scratch for mine out of PVC and a sock dryer ring.
It kept coming apart though so I just went to a rubber stopper on a leather leash.