So I bought some round-tips scissors at the drugstore, and gave him a bone to chew on. Then I contorted myself around his chewing head and did my best job trimming what I could.
The results definitely need some cleaning up, but my goal was just to shorten the fur without making it an unpleasant experience for him, since it was my first trimming attempt. Poodle owners everywhere may be shuddering at my butcher job, but he doesn't seem embarrassed (and I couldn't care less!):