2nd gen flooding as I attempt to start, every time
 

In the process of reviving this car, I ended up replacing the oem fuel pump with a new one from mazdatrix. Prior to said replacement it would start with some trouble but almost always successfully start cold but eventually die if I tried to drive it/stalled out because I turned the wheel. I replaced the p/s switch to fix that. But right now my issue is that with the new fuel pump, I can't even get it to start once. When I try to start, it while start to turn over then sputter out. It turns over less as I keep cranking. Then it won't at all. If I pull the sparks and deflood it then try again, the same thing happens. It starts to turn over then sputters out, flooding itself.

My guess is bad injectors that can't handle the increased fuel flow from a better functioning pump? I have a fuel pressure gauge installed in my bay in the line next to the oil dipstick, right after the filter. My plan is to replace the injectors as I have perfect fuel pressure up until them.

My question is what else could cause the car to flood consistently on startup? Could the FPR or FPD have anything to do with starting problems? When I unplug the fuel pump and try to start it, it starts and dies. I've also confirmed all four sparks fire. So based on that, it would seem I am just flooding it since it'll start with just the gas thats left in the fuel lines when I disconnect the pump, but if the pump remains connected, it is getting too much gas..

Your other symptoms may be flooding, but that sounds like a starter issue. Flooding won't stop your car from cranking.

EDIT: Also, come to think of it, low crank speed may make starting difficult causing flooding. Just a theory. Have you tried pull-starting it?

What is your pump rated at? Does it match the stock pressure nicely? Are you running a stock FPR?

I'm going to assume that you have a good battery and starter.
Assuming that the pump is stronger than stock and you are running stock FPR you could try this:

While cranking for a second or two floor it and keep cranking. Then after 2-3 seconds back off from floored position to half but don't stay there too long before you back to floored again. The trick is to cut fuel(floored) at the right rate.

Try different combinations. You might get lucky.

If you have an aftermarket FPR and you KNOW your settings then you're flooding for another reason.