Best way to order health checks for 500+ sites

The easiest way to make mass changes is from the CLI using tmsh. You should be able to prepare a file with the necessary commands that you can then cut & paste, or you could script the change.

Regarding the monitors, you should assign the site specific monitor and the server specific monitor to each pool and "Availability Requirement" on the pool should be set to All. If the site specific monitor fails it will pull the server down for the single pool that it failed for, if the server specific monitor fails the server will be downed for all pools.

Eric