I believe because of the continued moisture problem,
the thinset would eventually release the cementboard
and you'd end up with a "floating floor". All the parts
of your solution are also sensitive to ground movement,
which would also make the cementboard shear, and
the leveling compound will release. Leveling compound
is meant for a completely stable floor, and in the tile
trade it is meant to be covered right away- not as a
finish coat.

As others have said, you need to deal with the moisture.
Containing the moisture, as you propose, is very risky
and opens up other problems such as effloresence (sp?)
where moisture under thinset, cementcoat or grout causes
salts to leach out of the cement. I've seen this happen many
times, _always_ in the presence of continued moisture such
as you have.

The simplest solution I can think of is to skim coat it with
a mix of 50% flexible thinset (the expensive stuff), and
50% clean sand. Your floor should be super clean before
doing it, and consider painting a latex "link" on your slab
before doing it. As you skim coat it, scratch the coating
real hard into your floor to get a good bond. When I skim
coat, I use a notched trowel to scratch the coating into the
floor, then a flat trowel to level it. It's like if you drop a
booger onto your pant leg, you can lift it off, but if you
smear it in........it sticks pretty good......

Oh and as has been mentioned, de-umidifiers work great.
We live in Florida and used one in a non-air conditioned
storage room we had, and it kept the room dry.

Have fun,

thetiler