Yeah, I finally got it out after going through most of the naughty words in my dictionary. Lots of wriggling back and forth and finally applied a touch of sanitized water right around the lip. No ice brick or anything - would have probably melted off after two hours anyway. So I guess it was just an uber-tight seal.
Next time I will leave a bit more of the rod exposed at the top, enough to get a firm grip with one hand.