why not Sand Point up at Palmie Jethrow? Surely you're familiar with that spot. Free parking, deep water, a few boats to navigate but once you're out you have essentially the same stretch of water as Palm Beach itself without the hassle of the low tide mud. Alternatively just down the beach from palmie at the golf course although you may be fighting for a parking spot on occassions. Not great rigging area but a nice beach to launch from and NO mud down there.

have you tried manly harbour? there's free parking if you look hard enough although it usually means a bit of a hike with the gear, its more than deep enough although there can be a few boats to navigate past on the way. I've been out there in south east & north east. Ended up over at the quarantine station once with a broken mast...