Sorry to jump in your thread but yes. Maybe keep the "Sydney" tag as its near enough to Easts, but the logo has to go.
Maybe a stylised version of your old one is needed. My apologies to Tottenham, but it gives you the idea of what I recon you should use.
You could put whatever words you want in the ball, possibly "Easts to Win" and keep the name "Sydney". I think you should bang on about the 1908 thing too. Best asset your club has. , You could have a line drawing of the bridge or a boat or the opera house behind the chook too, would look good on a shield.
Retro is cool, cartoons are sh*t.