It's not just where the verb is; sometimes I say something ambiguous, and my next utterance is supposed to acknowledge and remedy that. But if that ambiguity doesn't exist in the target language, I don't see how a simultaneous translator can convey the ambiguity, without knowing how the next utterance is going to refer to it.
Maybe that's why human simultaneous translators often seem to stumble or backtrack. I've never met someone whose job was simultaneous translation. It must be very difficult.
I'm impressed by this effort to convey non-linguistic elements of speech in translation. It's quite an achievement, and a very ambitious goal.
Aside: I wish I knew how speakers of tonal Chinese dialects express feeling, when tonality is supposed to convey semantics. When I hear chinese speakers, I can "hear" the feeling, but I don't know how they do it - it can't just be down to emphasis. (I learned some mandarin 50 years ago, at school. I learned the tones, but they didn't teach expression; and I was never taught by a native speaker, although there were language-lab tapes.)