how does current work in an amplifier?

PS. I should mention that applying a dead short for smoking affect will require extensive repair of your amplifier. Also, a dead short will not hurt a transformer coupled tube amplifier, but would not be good for the tubes in an OTL version.

So.....all other things being equal (same room, same source, same cables, same other characteristics of the amplifier), am I to understand that an amp that delivers more current would do a better job of driving a 4 ohm speaker, like Magnepan MG12's, than would an amp with less current?

Actually, as 4 ohm speakers go, I think Magnepans are less current hungry than many. They do like lots of power though.

It just depends on the amp-speaker combination and how high a listening level you prefer. Once the power supply of the amplifier is maxed out, the output signal voltage is not going to be able to match the input signal waveform, ie. distortion. The bass requires the most power, so it is the bass that starts to sound flabby or weak. At least, that is my experience...

The KISS answer to your second question is YES. An amplifier rated for a continuous 4 ohm load should handle 4 ohm nominal speakers better than an amplifier that is only rated for a continuous 6 ohm load. You're probably safe to make comparisons within a brand, but I don't think advertised specs really mean much when comparing different brands.