The 200ft barge lanes are definitely inside the channel markers. See here
for more info. As stated above, if you stay in these shallower lanes and hug the markers, you don't have to worry about the big guys, and it's fairly easy to stay out of the way of any barges/tugs, although you might wind
up crossing back and forth a few times if it's a busy day.
Another option is to use "west pass", just S. of Redfish Island (circled). Location and depths here are accurate as charted, and there is a daymark on a piling marking the shoal. Go slow, and pass just west of the piling, and you'll be fine. From there on, there's plenty of water
to run all the way down the west side, keeping out of the HSC. There are a few stakes and (charted) wrecks to avoid on the way down, but it's a bit more relaxing than running the ship channel.