Think you meant birds on the trees shitting on your car... trees don't shit bro lol.
I get what you mean. I used to drive to Ginza all the time but it's such a hassle because all the spots are 1P only. Makes it risky to book a 1 hour or even 45 mins punt because you might get a ticket.
And you're right, very hard to find a spot because people who live there also park their cars on the street. The furthest I've parked when I was driving there was on the other side of Cleveland St and more than 2 blocks away... Think it worked out to be almost same distance to central station! I was desperate because I was running late for my booking with the lovely K Kiki. That was the worst.
These days I leg it there from the City or central station. If you absolutely have to drive, I recommend parking in a proper carpark near Central station, like the one at the corner of Elizabeth St and Goulburn St, then leg it down Elizabeth St from there. I'm sure there are better carpark options than that though.