I stayed at the Sacher in a Junior Suite in early October 2019. It didn't feel overrun by tourists at all. I really liked the hotel - would definitely stay again and recommend it. I saw Park Hyatt. Good location, but was otherwise pretty standard Park Hyatt style offering. Imperial I also saw - old world Vienna, but I wasn't a fan of the location.
Sacher has a Virtuoso comp 3rd night at the moment so might be worth swapping from FHR. Virtuoso at Sacher is upgrade at booking too.