Given that the ITCZ can extend for hundreds of miles it might not be possible to fly around it, even if you wanted to. Therefore, you have to work out how to get through it. I've not been that far south but my strategy when I have to punch through a wall of CBs is to is to look for the tops and go inbetween. Before entry I'll confirm that the way looks good on the radar. But to get a reasonable picture you may have to manouevre the aircraft so you are perpendicular to the line. I try to use the same strategy at night but it can take a little longer.
PM