G'day GET,
Basically any time you fly through the tropics and over the equator you're pretty much going to pass through the ITCZ. I have passed through the ITCZ many many times over the last 30 years or so and it can be done quite safely and is done by hundreds of airliners every day and night.
The picture shows the great circle track from Miami to Buenos Aires, which as you say is mostly over land.
Regards and enjoy BA,
BH.