I have come across other ideas, most of which require the DB being in single user mode

ALTER DATABASE TestDB

SET DISABLE_BROKER

ALTER DATABASE TestDB

SET ENABLE_BROKER

ALTER DATABASE TestDB WITH ERROR_BROKER_CONVERSATIONS

ALTER DATABASE TestDB

SET NEW_BROKER

WITH ROLLBACK IMMEDIATE

I don't know if the top two would remove messages, but perhaps the next two would. What would be the fallout or problem with executing the bottom two?