Which automatic HDMI-switch with RCA audio-out will fit my needs?

Question

I would like advise on what specific HDMI switch I should buy. Here I assume a special HDMI switch will solve my problem, but I could be wrong.

My requirements:

1. I'd like a switch with a minimum of 3 HDMI inputs, forwarding up to 1080p.

2. I would like analogue audio of the active HDMI input sent to my stereo, accepting RCA.

3. I would like the HDMI switch to automatically select the active HDMI input.

4. Specifically I would like to have my TV show the output of my PlayStation when I turn it on.
5. Specifically I would also like to have my TV show the output of my ChromeCast when I start casting to it.
6. Specifically I do not want my TV to show ChromeCast's pause screen when my PlayStation is turned on!

The last point is there because it's a point I'm concerned about. How do automatic HDMI switches handle a continuous input signal when it's actually an idle signal? Do they select the most recently activated HDMI input if more are active? Is there a pause priority property in the HDMI specification that ChromeCast will use when idle - and if so, does it work?

I've found this device which comes close to the above requirements, but I'm unsure about how it handles #6. I was going to ask the manufacturer, but I'd still like some feedback from you guys first.

I hope the above makes sense. Thanks in advance.