As previously stated, a mooring is about as good a place to be in a H'cane as it gets. Best place would be a hurricane hole waaay up some creek, but even that idea can backfire on you. At a dock there are a lot more things that can go wrong that are out of your control.
You are going to need chafe protection for your mooring lines. This is essential!
This is what it looks like: TAYLOR MADE Dock Line Chafe Guards at West Marine
Buy some. Buy more then you think you need. It is cheaper than a haul out and well worth it.
All bets are off if there is a 20' storm surge - which is not likely in Narraganssett Bay, in my opinion IF the storm track towards NJ/Delaware as currently forecast.
If you had the boat hauled and there was only 12' of storm surge your boat might get knocked over in the boat yard by the rising water. Basically, you are safer on a mooring IF it has the scope to handle whatever storm surge you get.
Don't over think things. Sometimes ideas that sound good can have unintended consequences. Your best bet is to follow conventional wisdom at this point. This is no time to be trying untested ideas.
Deploying your anchor while secured at the mooring with a big blow coming is not a tried and true backup plan. Your anchor line may wrap around your mooring and cause it to fail or the anchor line may lead a runaway boat right into yours.
The given advice to remove your anchor from the bow is the best practice. Remove all sails and anything that adds windage (boom, sheets etc.) and depend on your mooring to keep your boat where you left it (hopefully).