The only way I can think to do this might be a little hokey. Is everyone hearing only half the prompt? Sounds like something you might try investigating on the switch/CCM side.
You could try having the routing rule send the calls to a call handler instead of directly to the Attempt Sign-In conversation. Then you could set a blank greeting (with as much silence as you need), and set the After Greeting Action to Sign In. If you want this to work all the time, you should enable the Alternate greeting and set these up for that greeting. If it's enabled, the Alternate greeting will always play regardless of schedule, overriding other enabled greetings.