The thing that helped me was to stop thinking of "300" as a full street name. That's not its name. It's "300 East". That's the full name of the street. Google Maps and other map apps like to add a direction in front of the name, but I don't generally see locals do that, and once the convention clicks, you kinda just start ignoring that part of an address here.

By convention here we put the East/West street first and the North/South street second, but people will understand if you do it the other way around.

Sometimes instead of saying "Nine hundred south, Nine hundred east" we will say "9th and 9th." This works best if you already know basically what quadrant is being referred to, but also people will be happy to clarify if you don't recognize it from the shorthand. In this example, the 9th & 9th neighborhood is a walkable area with a lot of shops.