Hi,
I'll be pleased to work on this project for you. Let me introduce myself. I'm a CCIE certified network specialist with 6+ years of experience in configuring, troubleshooting and maintaining complex networks for large enterprises.
I recently did a project which was exactly like your project: it involved casting to a different subnet. This can be done using MDNS repeater function of routers (new chromecasts use MDNS instead of DIAL). Please send me a message and I can explain it in more detail to you.