I'm not sure about any city ordinances or laws regarding fliers for your location. While you cannot place them inside the mailbox, it's possible you can insert your fliers into their screen doors. I'm not quite sure though how people would take to having fliers left around their doorsteps.
If there are any local stores within your delivery area, you could ask the owners if you could place your flier on the inside of their store front window. Better yet to purchase a plastic flier stand and ask if you could leave it next to their register. And in that flier you can perhaps draw a map of your delivery areas.
And while you don't want to knock on doors and disturb others, that might be one of the best ways to specifically market to those blocks and customers that you can deliver too.
It would be wise to have a friend go with you, and make sure your family knows exactly where you are for safety reasons.
I know if someone came to our house with a box of samples and offered me one, I probably would place an order right away if your sample pastries were good tasting. In your flier try to have some pictures of what you bake, along with a telephone number so customers can easily place an order.
And not to nag at you, but be cautious in everything you do out there.
I wish you great success!