Re: Engine dies, starts right back up
Good info! Being able to duplicate it at will is excellent.
Happening at such a slow speed makes me think that the TC (torque convertor) lock-up isn't supposed to be happening, but if there's an error in the tranny, say from a bad VSS (veh speed sensor) or a bad VSS signal (like a crushed wire, or shorted to another or ground), it leaves room for this to be possible.
You also have a MAP (manifold absolute pressure) sensor - basically a vacuum sensor - that could be causing issues by a bad signal, or lack of one. It could be causing the TCC (TC clutch) to engage improperly, pulling the RPMs too low.
The evidence of the lights and blower dimming suggests something like you're thinking, that something is sucking too much power, or that with that much of a load on the alternator, the engine speed being too low means that the alternator can't keep up with the load and you're depending on the battery to make up the difference. Since the battery is more like a glass with a valve at the bottom that flows electrons, if the alternator isn't pumping more electrons in the top it'll lose capacity as it drains. If the load is bigger, i.e. lights and blower, then the voltage drop is bigger, too.
Look for a dirty or loose battery terminal or grounding cable. Look for a dirty, loose, or frayed charging wire at the alternator (the BIG one). If the alternator's output can't get to the battery easily enough then any load on the battery will be amplified as it increases, resulting in dimming lights and/or slower blowers.
Make sure the grounding strap from the engine to the frame has been reinstalled tightly and makes a good electrical path. If the mechanics just threw it on any bolt but didn't make sure it was clean, the resistance can be part of all of your problem.
Lots more to look for, but you've done a great job narrowing it down. Please, please, please share with us when you finally resolve, okay? Even if it's something completely different from where I'm suggesting. I don't have a problem with being wrong, I just don't want to do nothing. Keep using the evidence you collect and you'll get it!