This may be tough because it sounds like you fired the parts cannon at it, and could have inadvertently added additional problems.
1) Are there any code that you know of. With a light, or pending?
2) Do you have a scan tool can look at some of the PID's (car data)?
3) When you start the car, put your hand over the tail pipe, do you feel some good puffs of air coming out before it stalls?
4) Try a different key, maybe the chip in the key is flaking out or failing.
5) Was there any work, no matter how minor, that was done to the car shortly before the stalling started?
I'm agreeing with pimperell, and leaning towards some type of fuel issues.
You said you've replaced the fuel pump and fuel filter? Aren't the fuel pump and filter one unit for that year? I don't have an 07 so I might be making stuff up