I don't know where Mangles Bay is. The stated depths should be mean low water springs, effectively the lowest tide you should expect. As you note in some circumstances it might be lower, highly unlikely as a very low tide has to occur at the same time as the environment goes against you.
The depth under the keel you need depends on a few things, the lowest tide, exposure to wave action, is the bottom soft mud or rock. You obviously don't want to bottom but if there is only a cm or two in it in the worst case it probably won't matter if it is soft mud.
Tell the mooring man your draft and tell him to give you a suitable spot.

Had a mooring there 4 years ago, very very mean in north wind! If you want sound avice consult with Offfshore Moorings, they have the best knowledge of the area, I had a 13ton ferro yacht for 3 years on one of the moorings they installed and it never moved an inch, the concrete blok was anchored with 2x 50m lenght of heavy gauge chain going in 90 degree angle in a north and west direction.
my mooring was 2.7m deep and my boat draft was 2.3m at some point it was rubbing the bottom (i could see where the grass had been peeled under the hull).
Also be sure you have a decent dinghy, I had a small 3 HP powered tiny and I got stuck for 2 days on my boat as the wind was so strong I could not go back to shore.
Do you like sea birds?
Make sure the mooring is registered with the dept of transport as well!