After 1/8 to 1/4 mile, the engine just shuts off?

The engine starts right up and idles and revs great. It is a Z24 with a five-speed stick. However, when I start to drive it, after 1/8 to 1/4 mile, the engine just dies, this under acceleration -- either slight or heavy, or even driving slightly above idle RPMs. It won't start until about 2-3 minutes later, fires up just fine, but shuts off again.

I threw a few parts at it: new fuel filter, fuel pressure regulator, IAC, spark plugs, oil, air filter. The MAP sensor is good, though I haven't checked out the EGR.

It acts like there is not enough fuel getting to the engine. So, I Tee'd a fuel pressure gauge to the fuel line from the fuel pump so I could view it while driving. To my surprise, the fuel system held a constant 35 psi all the time, never wavered. Now, I'm not quite sure where to test next. Is it electrical? I'm not sure because sometimes when it stalls and after I keep the motor spinning (clutch engages) when I let the motor stop spinning, I get a backfire. Also, if I keep the clutch engaged, when it has shut off, the engine acts like it has been turned off, no sputtering or anything. I would understand this to possibly indicate adequate fuel but spark problems. But then why does it come back to life after the same amount of "down" time every time?

The thing is, it runs and revs and idles so smoothly, hot or cold. The is no check engine lights or error codes. I have many years auto diagnosing experience and I am a Mechanical/Electrical engineer. This one has me baffled and I don't want to tear it down without having path to follow. I'm thinking maybe "coil" issue? Help