Paul, you will need to multiply your budget by 10, then revisit this idea. To do what you're asking is not cheap....even for 1 camera. You may be able to accomplish this for 1 camera via cables for $1k, but it would be an entry level solution at best.
And even then, your Handy-Cams would be the weak-link in the setup...kinda like having a Ferrari & putting 25$ used tires on it.
When I think wireless HD video, the first thing that comes to mind is the Cube rig from Teradek.
If you want wired, I'd check into the Black Magic ATEM camera converters.