Sounds like you've got the right stuff, Sheila! But 1700 miles away...
I didn't get around to calling my local Autozone today to ask what tools they have for rental, but now I may need one less rental tool for this job (I detail this at length below in case it helps any other relative beginners who also get stuck with a stuck nut/bolt):
Tonight I was successful in removing the nut that holds the alternator pulley in place, without using an impact wrench (though that probably would have been a lot easier--some people even find using one doesn't require you to clamp the pulley so it doesn't move). I squirted two more brands of bolt-loosening fluid onto the nut and bolt, just because they were in my garage (Liquid Wrench, and an older type called "Sprayon"), then I tapped the nut/bolt lightly with a hammer a few times to work in the fluid. While letting that soak in for a while, I tried another method for holding the pulley in place so I could turn the socket wrench without turning the pulley: I gripped the pulley from the side with vice grips, and wedged the end of the vice grip's handle into a hole on the shock absorber mounting bracket (the bulge at the corner of the hood cavity). This held the vice grips and pulley in place pretty solidly, but as I soon found out, not as solidly as I needed. But the nut still didn't budge using my socket wrench, even when I hit the handle of the wrench several times with a hammer (trying to simulate an impact wrench! Yes, a crude substitute, I know). For a moment, I thought of getting more leverage on the socket wrench by lengthening it by placing a metal tube around its handle, but for some reason I immediately forgot. I blame the Liquid Wrench fumes.
Next, I used a propane torch to heat up the nut and its bolt, to try to break the molecular bonds holding the two together. I heated them for about three minutes on a low torch setting, then I waited for them to cool a little to let the bolt contract in size, then I heated just the nut to make it expand, and then I tried turning the nut with the socket wrench again. It still didn't budge, and the vice grips slipped out of the hole I'd wedged its handle into.
I was beginning to think it might be easier to just go to my local Pick N Pull and get an alternator with a pulley already installed, out of another Taurus, but I really didn't want to take the chance on an alternator in unknown condition, and I didn't want to buy a new one (about $100-$190 for a decent one), since as far as I can tell, mine is working fine (charging the battery, etc). So later in the evening, I tried again to remove the nut. I sprayed on some more Liquid Wrench, then I found a position for the vice grips that was more solid than the way I'd mounted it earlier--I clamped it to the pulley vertically in front of the body of the alternator, with a jutting part of the vice grips fitting against one of the alternator body's external vanes. Then I used the propane torch again to heat just the nut, but this time I turned up the torch a little more, and got the inner, brighter blue point of the flame right on the nut, moving the flame around the nut's entire circumference, for about two or three minutes. Then quickly, before the nut had time to cool and shrink, I put the socket wrench over the nut, and pulled on it for all I was worth, willing to risk skinned knuckles. The nut budged very slightly. I tried twice more, and it moved again very slightly. I tried a third time, and the wrench slipped off and I hit my head on the underside of the hood. I touched the nut (not my head) to feel if I had rounded it, and I noticed it was loose. I manually twisted it off its bolt (there was no resistance now), then easily slid off the pulley.
This may sound like a small accomplishment, but for me it's both small and major. I've done all this in the past for a few stuck bolts on non-cars, but I didn't think I was going to succeed with this. Now all I have to do, is repeat the procedure at Pick N Pull to get a replacement alternator pulley, and hope the process is no worse there. I'd buy a new pulley if they were easily available, but they're not, and they probably cost a lot more than I want/need to spend. Autozone doesn't carry them, and O'Reilly (formerly Kragen) has to special-order them, and they haven't gotten back to me with a price yet (no doubt it'll be a case of, "If you have to ask, you can't afford it"). I might spend the money on a new pulley if the Taurus 3.8L engine and its alternator could take an OAD-style pulley (an overrunning alternator decoupler), which I just learned about--on the correct engine, it can smooth out the belt: