See, I think it's much more polite, and warmer, to directly say, "I'm going to have to send you home, unfortunately. I'm zonked, and need some time to myself. This has been fun. Here's your food."
It feels much less critical.
The underlying problem is that it feels
rude to ask someone to leave. Many people have been taught that it is
rude to say something like that. It's not. It can be said rudely, but the idea of asking someone to leave when they've overstayed their welcome isn't rude at all.
Someone who stays when the host is giving clear signals (i.e. cleaning up, yawning) is being rude. There's no need to retaliate with rudeness, but setting clear boundaries with polite wording is fine.