I don't know an LLM that does context based rewriting of interpreted text.

That said, I haven't run into the icecream problem with Whisper. Plenty of other systems fail but Whisper just seems to get lucky and guess the right words more than anything else.

The Google Meet/Android speech recognition is cool but terribly slow in my experience. It also has a tendency to over-correct for some reason, probably because of the "best of N" system you mention.