From my understanding worm gears are not all that inefficient if used in certain ways. Judging by what it says on this site:
http://www.roymech.co.uk/Useful_Tabl...orm_Gears.html
you can achieve a decent efficiency of 70% or higher using a bronze wormwheel and 2-lead steel worm if they are turning ok, and should not backdrive either.
That being said, worms and worm gears are expensive. Furthermore the only place I've found that has a decent selection is SDP-SI and wmberg. If you go SDP-SI, they only have 24 pitch worms and worm gears in stock, so you would have to have another stage of reduction after the worm gear to reduce load on it, which would slow you down a lot.