I've got a number of Scheffleras and they all exude some sticky stuff
which
ends up on the carpet around the pot. It does wash out with carpet
shampoo,
but this is not something I want to do more than I have to. Does
anybody
have any suggestions for controlling the sticky stuff, or getting it
off the
carpet without having to drag the carpet shampooer out?

The sticky stuff is likely to be caused by some sap-sucking pest,
probably scale insect. If you can eradicate the pest, you'll get rid
of the problem. This probably means spraying with insecticide/fatty
acid. You could also wipe the bugs off with cotton wool dipped in
methylated spirits, but with a schefflera it would take ages and there
are always one or two scale insects that get missed.