P0300 on Cold Start, P0456 Then Stalls

ENGINE/DRIVABILITY
Idled Fine, Ran fine. Stalls on Cold starts when Temp is below 55 F
Year/Make/Model: 08 MazdaSpeed 3
Mileage: 1005423
Location: NW Missouri (KCMO)
Concern: Misfire on start up (with smooth idle), NEW: on cold start will stall (Will start when outside temp is +55 F)
DTC's: P0300, P0456
Modifications: Cork Sport HPFP (code p0300 happened before mod), Mazdaspeed branded Cold air intake (GRMS-8M-L29) and exhaust (GRMS-8M-L02)
ECU/Tuning Software: Stock Tune
Tuner: N/A
Is the concern intermittent? Yes(P0300)
Can you duplicate the concern? Yes
Recent Repairs: New Plugs NGK Gapped @ 0.028, Ran injector cleaner (BG44K PLAT)

The P0456 started today 9/12/2023 (Yes the gas cap is tightened) and the Random misfire (P0300) has been happening for a few months and the car has ran great even with the RM code popping up every few hundred miles or so. I have browsed the forums and after the 2nd code popped up I have decided to make a post. Most of my time driving it is on highway with cruise set to 70-75 for about 40 minutes every morning. After the P0456 ive been getting very quiet backfires

 

How recent was the spark plug change? Might need to pull them and check that the gap hasn't opened up

 

The plugs were changed ~4 months ago

 

i would pull them and check the gaps

 

The gap is the same and hasn't moved. I'm personally suspect of the gas tanks fuel pump because when I run it, its popping like it's low on gas. But that could just be me

 

Here is a video of it starting:

 

Check the purge solenoid. Disconnect it's electrical connector and then remove the line from the tank to the purge solenoid. Run the engine and if you can feel a small pull of vacuum coming from it then it's not fully sealed when closed.

A leak can be internal in a system and not show evidence of smoke. Do you have any extended cranking issues after refueling?

 

I actually did that purge test a couple hours ago and it is working, and no it doesn't have an extended crank after refueling. One thing i just remembered that happened when the car was stalling on start is i tried pressing the gas pedal to give it some more gas to keep it alive but it didn't work. Hence why I'm still suspect of the fuel pump or something fuel related. I am going to buy new coil packs pretty soon (oem). I've been tracking this p0300 gremlin ever since the code has shown its ugly face, so I hope with your guy's help we can do that. I wish I had means to upload my logs, Is there any way to do that with a basic code reader?

 

When at idle the fuel pressure is around 418-431 psi the vehicle is warmed up.