My 1984 S&S34 on a Pittwater swing mooring is currently being insured with Club Marine. I was with Nautilus until June and they stopped covering boats on moorings. I understand Trident will also cover boats on swing moorings.
You need to understand what they actually cover. My research (pretty extensive 2 years ago) is that their liability is limited to your boat hitting or being hit by something. E.g. they don't cover your rig going over the side, no matter how new, if you didn't hit something.

I am also with Club Marine and my boat is on a swing mooring in Sydney Harbour.

And just to clarify my boat is a 1986 model.