I may have a working solution.
I'm using this:
and taking up 2 HDMI ports on my TV.
As it's not a switch, just a splitter, I have to power off the breakout box, otherwise PS4 defaults to lower HDMI standard. But the power switch is right near where I store the headset & other cables so that's not a problem for me.
HDR is now working on my TV which is damn nice. Haven't had a chance to use PSVR in last few days to check that there's no issues there.
You need to actually check PSVR will turn on properly. In my experience it doesn't play nice with splitters between the PS4 and breakout box. It'll turn on (as in you'll hear the beep) but it'll think you haven't connected it up properly and refuses to work until it has a direct connection.