How do I level a basement floor but not the slab underneath?
I can't imagine the sand idea working. I'd probably scratch that one off the list.

Is the basement dry? If you feel that you still need a sloped floor to deal with water issues, I think you want to tackle those first before thinking about finishing the floor. 

Otherwise, your shimming idea makes the most sense. I don't think pebbles will work but some form of furring strips may work. Get treated 2x2s or 2x4s and scribe them to match the slope. Then cut them and affix them to the slab (adhesive may be enough...otherwise you can nail them with a power-actuated hammer). 

You could apply the shims radially from the drain to accomodate any eventual water flowing to the drain.

For what it's worth, we have an old house and when we finished the basement I decide to be lazy and we stained the concrete floor. If you like the look, it's easy, cheap, and never any fear of a water-damaged carpet or subfloor. 

While the floor can be a tad cool in the winter, once the space is heated it's quite comfortable--especially if you put a rug down.