I've had similar symptoms on my '87 when I acquired my car, but not quite as bad a yours. Here's what was wrong with my car:
-Bad Idle Air Control Valve (flooded with oil due to a clogged Flame Trap).
-Fouled spark pluges (caused by the bad IAC valve mentioned above)
-A broken vacuum line.

Also, check these items since they can also lead to symptoms that you've mentioned.
-Mintature holes in the tubing/ductwork between the Air Mass Meter and Throttle body.
-Fuel Pressure Regulator (remove vacuum line and check for smell of fuel)
-Air Mass Meter
-RPM sensor (mounted in the distributor where the wire harness connects to it, below the distributor cap).

I would feel pretty confident that your Relay and fuel pumps are not to blame for this problem. The symptoms would be very different and you'd have more problems at all driving ranges. Also, if you can tell if your car is running rich or lean, that would help us out in diagnosing the problem further. This can be done by hooking up a wire to your Oxygen Sensor and running it to a volt meter. Don't run the car with the O2 sensor disconected since this will cause the car to run rich, -so add a wire at the point where the O2 sensor wire connects to the car's harness. You should get an average of 0.5 volts or so at Idle with a warm engine. A rich condition starts climbing upwards (max value would be 0.9 volts) and a lean condition would be lower (around 0.2 or 0.1 volts).

Good luck and God bless,
Fitz Fitzgerald.

P.S. A $25 vacuum pump is a great investment in hunting leaks and diagnosing vacuum parts.
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'87 Blue 245, NA 214K