Introducing a queen to a Q+ colony is bound to fail. Just do something like you describe - move the hive three feet or more away and leave anything in its place, go for a nice cup of tea, come back and all the fliers (which is the majority of the aggressiveness in your hive) will be in the new position giving you a much emtier and calmer hive to go through, find the queen and use her as a gatepost decoration. You can then either immediately introduce the new queen in her cage ensuring the bees can't get at the candy to release her.then move the hive back to the original spotb checking every few days to see if the bees have 'taken to her' before giving access to the candy.
Alternatively, on disposing of the queen put everything back as was and ensure the colony is hopelessly queenless before introducing the queen in the same way.But make sure you take down each and every emergency queen cell