Hi Parking Mad,
I understand how you feel because parking in my street is a nightmare, and I often cannot park within half a mile of my house.
Unfortunately, you do not have a legal right to park outside your house, nor do the council have a legal obligation to provide parking for you.
At the end of the day, you are parking illegally, and will have to pay the fines.
I have read several stories about people challenging fines due to no stop lines, and some of them have taken their cases to court, but I cannot think of a single one that managed to overturn the fine.