re: 1 coaxial, 3 RCAs, 2 hdmi, all into a single hdmi?

Something like that might exist, but that's a level of specific that might cause you issues. With that said, there are RCA switches like this:

LINK

That you could then run alongside a separate solution for the rest, like a simple HDMI splitter.

ETA: Now that I've had a few more sips of coffee and read your OP again, I now realize that solution won't work for you at all. That's... a tall order.