VariAudio can sometimes create a garbled sound on certain notes. I've not discovered a consistent pattern to the problem. It's just something you have to be aware of - editing the pitch detection bars usually cures it. The longer you spend editing the pitch detection before applying any correction, the better the results are. Often I'll reduce the corrected portion to a fraction of the overall note length and that's enough to sound corrected without sounding obviously processed. Removing detection from consonants and breaths is not always necessary, but if you spend the time doing it you're more likely to get something you like at the end.
Multiple parts are fine. If the going gets tough for your computer then you can always flatten the processing.
And yes, correct only that which needs correcting.
An Eagle for an Emperor, A Kestrel for a Knave.