WOW! jakeru has described that Very well (almost felt like I was seeing it )

I would just add two things. I would "lean" the torch towards the 3/8ths piece, concentrate the heat on IT, maybe start the weld on that side and once a puddle is established there, run it to the 1/16th and proceed like that the whole way.

And, with Aluminum in general, the problem we have is that it takes a "practiced eye" to recognize when things are just starting to go wrong (unlike steel where you get a color change towards White and "sparkling"). Things happen Fast, too much heat in the piece has accumulated as you get to a place where it's no longer being dissipated or it's just "built-up" and backing-off the Amps alone isn't gonna save it... But Filler Rod might! Be prepared to stuff 1-1/2" of rod into the puddle at any time! -hehehe...