Finally,
SUCCESS!!!
I took the 'argon' bottle back to the supplier today, and they were easy about swapping it for a new bottle. They looked a bit incredulous that it would be contaminated, and one of the guys there said he had never seen a contaminated bottle in all the time he's worked there... Before I brought the original bottle back, I tried just striking an arc on a 1/4 inch coupon of 6061-T6 to see what it would look like, since all the other 'experiments' described above were all on HR or CR low-carbon steel. I'm including that picture below. It was nasty! I brought the coupon with me to show them, just in case they needed 'proof'.
With the new argon bottle, I tried a few no-filler passes and a few with ER5356 Al rod. The difference between what I had experienced with the old bottle and the new bottle was like night and day! Amazing! The arc was stable (no frothy splashing), a nice controlled puddle formed, there were no volcanic streamer sparks, the bead and area around it were clean (no soot), it even sounded different, a nice, satisfying buzz. So, yes, one can get a contaminated argon bottle, even from a reputable supplier.
So, I'm on first base now! Thanks for all your help to figure out what was going on. Now it's time to burn some rod and get some practice...