How about a grid system that changes direction at every single avenue?

Looks like everyone started a new road perpendicular to the shore line, and the mess occurred when the roads got long enough to meet.
Bingo. Allow me to introduce you to the colonial French seigneurial system.
Seigneurial system of New France - Wikipedia

No they’re were designed that way. The names remain the same no matter how many times they turn. The street i live on starts off going west, then south, then south west and back to west again on the other side of town.

Speaking as someone who has been living in towns with rivers for most of my life:

This is the way.

My experience clearly says that you will loose orientation and get confused the moment you go to a district that is not alligned with the riverbank.

Still a better system than Boston, having navigated both MANY times. To call Boston’s streets a “system” is an insult to the very concept of order.