I have a 2004 Honda shadow spirit 1100. When I open up the throttle to accelerate the bike starts to backfire and loses power. This mostly occurs on the interstate when i'm accelerating from 60 to 70 or up. Not sure if its related but I just had the charging system replaced a few weeks ago.
I wish I could give you a more exact answer, but I had this issue on a Harley of mine a few years ago. In and out of the shop for 2 years or so because it would lose charge in the battery overnight, where I had to remove the main fuse when I got off just to prevent it from happening (annoying, but better than another couple months in a shop where they can't find a fix). Then I started experiencing a similar problem (to my memory) as to what you describe.
I seem to remember it being an alternator with a bad wire. So if you say you just had the charging system replaced, then maybe there is some truth to my memories about it.