I'm stumped, but also sort of slow, so it's okay :)

I’m assuming that your car has an automatic transmission. The distributor doesn’t have a mechanical advance. The distributor rotor is held on by a screw.
Fuel pressure is a suspect for the stalling on acceleration. A dirty fuel filter will drop fuel pressure. The fuel filter is in the engine bay, on the fire wall. It’s fairly easy to replace.
If there is corrosion on the battery posts and cable terminals, the full charge of the battery can’t get to the battery. A jump battery cables are attached to the outside of the cable terminals. That current, from the jump battery, doesn’t have to try to go through the corrosion, so, it has no trouble starting the engine. Remove any corrosion from inside the terminals.

Hello all!

I have very happy news! Today, after my laundry adventure I headed out to the auto parts store to buy new plugs, wires, and distributer cap. On the way, I thought to myself that it probably wouldn’t hurt to bring the car on into the nearby DEQ (Department of Environmental Quality) inspection station on the way. I did this and the car passed on the first run (not what my original question was about, but a big plus anyhow). The staffer who tested my car suggested that a ‘great reward’ for my car would be to go ahead and change the plugs and wires. I kept trying to get the car to repeat the stuttering action, but it just wouldn’t happen. I got to the parts store (an AutoZone) where they tested my alternator, and found it to be kicking out 14.1 volts, so that should be just fine… After changing the plugs and wires, (I ended up skipping on the cap… I’ll have a little more cash in a few weeks- perhaps I’ll do it then).

So I would like to give a big thanks to everybody who pitched in with their advice! Thank you! Thank you! Thank you!