Service Broker SEND performance
Perhaps the routing configuration change didn't take effect immediately.  To be sure test with a new broker.  Try this from a database other than the database containing the target service:
CREATE EVENT SESSION [ServiceBrokerRouting] ON SERVER 
ADD EVENT sqlserver.broker_dialog_transmission_body_dequeue,
ADD EVENT sqlserver.broker_dialog_transmission_queue_enqueue,
ADD EVENT sqlserver.broker_forwarded_message_sent,
ADD EVENT sqlserver.broker_message_classify,
ADD EVENT sqlserver.broker_remote_message_acknowledgement

GO
ALTER EVENT SESSION [ServiceBrokerRouting] ON SERVER STATE = START;
go
DROP ROUTE [AutoCreatedLocal]
alter database current set single_user with rollback immediate
alter database current set new_broker
alter database current set multi_user

--Watch Live Data on the ServiceBrokerRouting event session
--test to ensure that new messages are delayed

--add the forwarder route
CREATE ROUTE Forwarder
    WITH  
    ADDRESS = 'TCP://localhost:4022' ;   

--Watch Live Data on the ServiceBrokerRouting event session
--test to ensure that new messages are routed through the transmission queue