DIYbanter - prepping for floating floor

I have read a number of posts regarding self-levelling a floating
floor.
In my case, I am working in a slightly below ground apartment suite
that has a concrete floor. The room I am working in dips 3 inches over
about 12 feet. I am trying to put in a floating floor since the old
carpet was hideous, but do not want to create a mammoth job for myself
as it is only a single bedroom and does not justify an extensive amount
of work or money.

** For the pragmatic among you:

My initial hope was to simply ignore the slope. Although it would be
nice to have it level too, I was more concerned with dips and valleys.
If I am willing to put up with a slightly uneven floor, I assume that
the primary drawback is 'bounce' in the areas of the floor over a
valley. I have also seen quite a variance in 'allowable' flatness
variations. I recognize that a 'proper' floor should be something like
1/8" over 8 feet, but have also seen posts that pragmatically
indicate that even dips of 1/8" over a couple of feet may be
acceptable, particularly if one can secure down the middle of these
sections to make them less mobile. Also, I was wondering if
realistically one can get away with less evenness in the direction
perpindicular to the direction that you are laying the floor. I
realize that this is all a little hacked, and not officially
recommended, but would appreciate any feedback on these ideas -
including future problems that any of these 'hack solutions' may cause.
(I don't mind losing out on the aesthetics of a perfect floor, but
want to clearly understand any 'flaws' that I may decide to live with).

** For those who maintain a 'do it properly attitude', perhaps you
could comment on the options below:

By the sounds of it, one option is to fill the room with a layer of
sand screed until it is close to level, and then (optionally ?) use a
self-leveller to make it even truer. (this would bring the concrete
slab above the low end of the drywall - I assume that I would leave a
3/4 inch gap or so between the edge of the new concrete and the wall -
is this ok?).

I was wondering, however, if it would be a little easier (or advisable)
to simply toss down some plywood and shim it where necessary to achieve
a fairly even surface. This would also allow me to secure down any
sections that may still 'bounce' a little if the end job is not
perfect.

The dip also rises again as the floor goes into the bathroom (where I
was hoping to lay tile).
This may also affect the decision above...(?)

Thanks very much,

- RG