Need to rent a moored boat

Check AirBnB.

Check AirBnB.

Did you check that? There are several between STT/STJ but none on STX as far as I can see,

No, didn't check, but it's a good place to check. New listings are added frequently.

I'm moving to STT, although I suppose I would be open to STX if it were substantially cheaper. How does living on a boat work?

You want to live on one, but don't know what its like?

Check AirBnB.

I can't find any boat listings on AirBnB. What am I doing wrong?

https://www.airbnb.com/s/U.S.-Virgin-Islands?type=boat&s_tag=y2dGTM3b

For some reason that link when copied and pasted doesn't come up. Just type "airbnb boat rental us virgin islands" into your search engine and you'll find the listings.

There are some boats in St Croix that are for sale. You might want to contact them to see if they might be willing to rent their boat.

http://virgin.craigslist.org/search/boo

Living on a boat is more like camping, even on a well equipped boat. Space is a premium, and if you are living with anyone you will get to know them intimately, smells and habits. Be prepared to bump you head and stub your toes daily. I'm not trying to talk you out of it it's just the way it is. The advantage is if you don't like your neighbors pull up anchor and move. Also being lulled by the sound of the wave at night is a plus. Another is having a cocktail or coffee (depending on time of day) sitting on your boat bobbing around. "If you're lucky enough to live on the water you're lucky enough"

If on mooring it's necessary to have a dinghy.
No one will let you sail any boat you're renting.
Have you thought this thru?

One other thing I forgot was if a storm hits you will need to move your boat or hope for the best. There are many boat the are for sale that are not on craigslist. You will need to come down and ask around many boats are for sale but only by word of mouth. Have you ever lived on a boat?

You may also be misunderstanding the terms here - a moored boat is one on a mooring away from the docks in a harbor -- it is not a boat that is in a slip in a marina with electric and water and possibly cable supplied - a boat in a marina is certaily more convenient to live on but is also certainly much more expensive.
Living on a boat on a mooring you will have to consider how and where you will charge the batteries for power and how and where your fresh water supply will be and also disposing of your waste water if there is a holding tank, replenishing the propane for cooking, fueling the engine if you have to run it for the power requirements and what kind of refrigeration is going to be available or where you get ice - and bringing supplies and laundry by dinghy -- As well as the dinghy situation with an outboard usually that requires fuel and maintenance and often a dockage fee where you land it.

You may also be misunderstanding the terms here - a moored boat is one on a mooring away from the docks in a harbor -- it is not a boat that is in a slip in a marina with electric and water and possibly cable supplied - a boat in a marina is certaily more convenient to live on but is also certainly much more expensive.
Living on a boat on a mooring you will have to consider how and where you will charge the batteries for power and how and where your fresh water supply will be and also disposing of your waste water if there is a holding tank, replenishing the propane for cooking, fueling the engine if you have to run it for the power requirements and what kind of refrigeration is going to be available or where you get ice - and bringing supplies and laundry by dinghy -- As well as the dinghy situation with an outboard usually that requires fuel and maintenance and often a dockage fee where you land it.

This *-)

One other thing I forgot was if a storm hits you will need to move your boat or hope for the best. There are many boat the are for sale that are not on craigslist. You will need to come down and ask around many boats are for sale but only by word of mouth. Have you ever lived on a boat?

The owner will need to secure the boat.
The renter would have to find somewhere else to stay in the event of a tropical storm. It's not safe to stay on a boat in a storm, especially if you've got no idea of what kind of mooring you're on and know nothing of boats.

I've lost boating friends in storms.

I can feel a troll all over.
But plenty on abandoned vessels in Benner bay. Just move in and live like a renegade. Bunch of boats on CL for sale that look like less than 1 year of rent. And then there is AirBandB.

I can feel a troll all over.

Before calling someone a troll (which is very nasty), check their previous posts. Obviously the OP is NOT one. Has the option of living on either island. May well not be happier living on STT over STX - but not a troll.

I'm aware of the differences of mooring and and a slip. I can sail but I would also be open to living on a boat in a slip for a month or two. May sound weird, but it's on my bucket list and my job in the islands ends at the end of December, when I'm returning to the mainland.

I'd rent a boat for $800-1000 a month, if someone has something.

Your best bet might be call Independent Boat Yard or Compass Pt. Marina offices on STT to see if they know of any liveaboard boat rental situations. You may actually have to visit, check the bulletin boards and ask around.
I know there have been rentals in the past that would suit your bucket list but don't know of anything offhand.