Rowe cells are often used for testing of reconstituted clays. They can be quite hard to come by, however.
If you have to start above the liquid limit for some reason then you'll need to do your sample preparation in a mould mounted on the triaxial apparatus, as EireChch suggests, because the slurry would be too fragile to transport.
The shearing stage of a CID on clay needs to be slow enough to ensure excess pore-water pressures don't develop. Adding sand will help the excess pore-water pressure dissipate more quickly, so you can shear the sample more quickly. It is this shearing stage of a clay CID which takes a long time; the consolidation stage is comparatively short. Also as EireChch suggests, two-way drainage will help speed things up a bit, though I wouldn't recommend doing it during the consolidation stage since you want to make sure your initial PWP reading at the start of shearing (i.e. end of consolidation) accurately reflects the PWP throughout the sample.