If you do a search on regulated phantoms, you will find an overwhelming preponderance of those who would say it creates either no change or worsens performance.
The reason is this...phantoms tend to work best at or around 800 or 850psi. Regulated HPA is coming out of the tank at this level...at most. The only reg you are going to find that does a good job at that high pressure level is a Palmers Stabilizer. The Stab will--at minimum--knock 100psi or so off your input pressure....so now you're at 600-700psi.
Bottomline, a 20oz CO2 tank is a lot better way to get great performance out of your phantom than messing with regs! YMMV