How to set-up Airport Timed Access Control such that Airplay keeps working?
Unfortunately not; Not without using another router with network Access Control Lists (ACL).

Airport's Timed Access Control rejects all connection attempts to the access point from selected device based on it's MAC address. It doesn't give you any options for more  granular Access Level Control in order to specify network resources the device will have access to; as you have probably noticed by now, you only have control over scheduling. 

A solution to your issue would unfortunately involve buying another router that will allow for configuring ACL to the degree you need it to.