I think im just going to go ahead and replace the fuel pump again and go ahead and put a new fuel pump relay.
^^^Hopefully this doesn't come across too hard. ^^^THIS is "parts changing" at it's worst. IF this problem is related to fuel pressure it is very easy to test for without having to buy parts and going through all of the work installing them.
Has the battery voltage been monitored while driving? If not there's a real missed opportunity to "hit one out of the park".
IF you just feel there's a part that needs to be replaced, then what about the alternator? Has it been tested for correct output (bad diode)? No excuse to skip this step as almost all auto parts stores will test for FREE.
What about the battery? Does it hold a charge? Are the battery terminals clean and tight? What about the grounds around the radiator core support?
Bottom line. Today's cars simply will not run right without a strong battery and charging system. Cut corners here at your own risk.
What has been done to rule out excessive EGR flow? Want a simple low cost test? Just remove and plug the vacuum line to the EGR valve. Does this improve symptoms?
Want to "KNOW" if your problem is related to the EVAP system? All you have to do is disconnect and plug the EVAP vacuum line and see if the symptom improves. It will cause a new DTC but that's OK as it's from the test.
What about the MAF sensor? If the MAF sensor were to suddenly report a much lower flow than actual, guess what? It would act just like the motor wasn't getting any Fuel......
Same thing for the fuel rail pressure sensor (FRPS). If the FRPS is in error it could "cause" an apparent lack of fuel.
Still think the problem could be related to the fuel pump relay? Monitor the voltage at the trunk mounted IFS shut off switch. IF this problem is related to the Fuel pump relay (CCRM), then it will show up as voltage drop at the IFS switch. IF the voltage doesn't drop at the IFS switch there's no way the CCRM is at fault. Problem only happens while driving? Then get a long piece of scrap wire and put the Volt-Ohm meter (VOM) in the passenger's compartment by lowering the rear seat.
Finally it seems to me rather than replacing yet another fuel pump on a guess, why not measure the fuel pressure? Even better. Why not measure the Air flow (MAF)?
Do you have a windows laptop? Do you have $30? Consider getting an ELM327 USB dongle with the ForScan software? Very easy to graph fuel pressure and MAF flow while driving. Then you will KNOW what is changing the moment the problem happens.
Expect a steep learning curve on how to use an ODB2 monitor to effectively solve problems but this is soooooooo much superior than changing parts on a guess. At the least wouldn't it be better to have an idea what's wrong before starting a repair?
ForScan ODB2 scanner w ELM327 USB
OHP Ford ELMconfig USB device 500kbit/s ELM327 compatible interface with MS-CAN switch for Forscan FoCCCus Mazda OBD2 diagnostics
View: https://www.amazon.com/gp/product/B01F0GVBWY/ref=ox_sc_act_title_1?ie=UTF8&psc=1&smid=A3HT224M59LA1Cie=UTF8&psc=1&smid=A3HT224M59LA1C
http://www.forscan.org/