Thanks for pasting the reply, tommjames - much appreciated.

The fact that in Slavic languages (my usual fallback) the given structure is illegal is what initially tipped me off, and it seems (judging by the Akademio's reply) that my intuitions were correct.

So what are our alternatives? I have two:

La du glasoj da vino, kiujn mi vidis, kiel ŝi malplenigis - Most obvious way to say this in a Slavic language.
La du glasoj da vino, kiujn mi vidis malplenigitaj de ŝi - Passive looks a bit clumsy here? Or OK? Do we use the predicative?

Most of the suggestions offered in this thread seemed either too wordy, or the emphasis was placed on the wrong details (e.g., stressing that I was at the dinnertable rather than stressing the wine that was consumed).