Experience is a mean teacher, but it would be a shame to waste all you've learned. Think of this as a chance to start over and do everything right.(sure) Maybe, do more stuff right. You have some extremely productive bees and plenty of woodenware.
Start with some diatomaceous earth under the hive(s) and invest $34 or a few hours in a Freeman bottom board. Clean and sanitize all of the old woodenware and give the hive a complete new home. Don't blame the mess on the queen. Blame it on the bee-keeper. You can do something about that.