Mac mini -> Onkyo 607 power cycling jacks up resolution

This is normal for HDMI switches. The EDID of your display doesn't get transferred after losing a connection.
You will need to reconnect the cable to the switch every time you turn on the device, or get something like this to preserve the information.

Nope. This is part of the HDCP standard in the core of the OS and hardware. Can't change that, sadly.

The link goes to Amazon in my post above...

I have having a very similar problem to this with my Mini and an Onkyo receiver. I looked at the product mentioned above but didn't want to spend the cash, my solution was to just plug the hdmi in the Mini directly into my TV and just send sound through the receiver. Combined with a harmony remote that sets up all my inputs it works perfectly.

I then had an issue where after rebooting the Mini the overscan was all messed up. The solution was to uncheck the overscan box, then check it again, basically cycling it. That solved the problem but was annoying so I just got an applescript to do it automatically and set it to run on startup. Now my Mini runs perfectly.

Hopefully these solution can help with your issue.

I use my Onkyo receiver (not sure of model) as both surround sound and a video switch for my display. My display only has one digital in port (DVI) and I wanted to switch between 3 devices so having a device that can remember the EDID is essential.