I'm pretty close to you - in Royal Peninsula and park my car there (but only after sitting on a long waiting list). Before I got my current car park, I was parking in a car park on Baker St - would be a bit of a walk for you, but I really don't think there are many other options in this area.
EDIT: Just realised, in the Google map there is the "Hunghom Peninsula multi-story car park" - is that the one you're referring to which is always full? If not, would be worth checking out...
Google map link