All this points to one conclusion I would personally just get them instead of having to constantly worry. You need a stronger, more capable fuel system
HPFP Troubleshooting | CorkSport Mazda Performance Blog
Upgrading key components such as the fuel pump, lines, filters,.
If you did install and datalog a set, you wouldnt be questioning all this talk about a set of internals being able to flow more volume on the stock fuel rail.
Tune is needed if you're changing the amount of air and/or fuel entering and/or leaving the engine Hpfp internals do not change anything by themselves, they just ensure that fuel pressure stays in a safe. To keep it simple, yes you can To get more into details, its kinda pointless unless you plan on upgrading everything within the life span of said pump, such as fuel regulator, possibly lines if.
Not necessary but a good peace of mind If you have a way to log you can test your stock internals and verify they're holding pressure