'97 SL1 Dies Randomly

The title says a lot. I have a 1997 Saturn SL1 that has progressively been stalling more and more often. It doesn't stutter and then stall, it goes from robust engine power to nil. It's done it while at speed and while at idle, though most often at idle. ...related? I do burn oil.

I cleaned the throttle body and EGR to the best of my abilities (full removal. the throttle body is immaculate, the egr...meh) This cleared out a check engine light that recently came on, and renewed some life in the engine when it's not dead at the side (or middle) of the road.

I'm thinking fuel filter? Would this make sense? Anything else I'd be wise to consider?

1) Fuel pressure test
2) Battery & alternator load test
3) Catalytic converter back pressure test
4) Compression test
5) Ignition test

You are missing some Air, Fuel, or ignition on the power stroke.
A plugged catalytic converter can also choke your engine out.