In order to avoid this, operators should use the attended transfer option. It is not necessary for them to wait for the other party to answer the phone, however. The operator can push the transfer button, dial the extension they want to transfer the call to (without hitting the blind key) and then press the Send button. That will keep the Music on Hold playing for the caller and free the operator up to take the next call.
NOTICE: When doing the attended transfer, the callerID on the destination person's phone will display the callerID of the operator and not of the caller being transferred. The only way to transfer the call with callerID is to do a blind transfer, which has the problems listed above.