How to set-up Airport Timed Access Control such that Airplay keeps working? I just tried using Airport Utility's Timed Access Control for my Airport Express and MacBook Pro.
Unfortunately the Airport Express cuts out all communication with a device during the restricted time, including the Airplay "channel".

Is it possible to configure the Timed Access Control such that only WAN access is blocked and the Airport Express is kept working in "LAN-mode"?
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.