I haven't touched a Harmony in many, many years. As tomciara suggests I would create a nonsense device and send it commands in order to create a delay. If the Harmony is really smart and multitasks, you'll need to use the same emitter port for the nonsense device as is used for the device that needs the delay.

In order to help this cause, you could "learn" some special IR codes that are deliberately concocted to be long duration.

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I assume that Harmony does not support conditionals. If this is the case and you understand the "State Machine" concept, you might be able to create a matrix of identical looking Home pages that include minimum delays appropriate for the current "state" of each device. This would not be a perfect scheme if something gets out of sync, but you could have a "System Off" button that would reset the devices and the state machine.

I would not want to maintain this sort of beast, but it would be a way of satisfying the customer's demand of being able to tinker with favorite stations and such. Good luck to everyone if the state machine is broken by the tinkering.