Hooray! My Krups La Glaciere ice cream maker isn't busted after all! An impatient cook has learned that patience pays, as far as ice cream makers are concerned.
I followed the advice of several helpful chowhounds: freeze the container in the BACK of the freezer (in my case, for 48 hours), make a mixture without honey or booze, and thoroughly chill the mixture (I fridged it overnight).
The result: My blood-orange sorbet froze in 8 minutes. And it was delicious! It was just juice and a hint of sugar; hard to believe that it could be better than the juice alone, but it was.
Thanks to everyone for their advice. I'm confident that adding a hint of alcohol or honey to the next mixture will be a success. (I've got a recipe for ricotta-honey-Grand Marnier ice cream that sounds quite promising.)