Ah, so you CAN split the HDMI signal to avoid using the processing unit.
Using one of those "4K 3D" video splitters, you can input the HDMI and then send one output to your receiver/TV and the other to the PSVR box.
There is a catch, however, in that, while you can still use your receiver for audio, you can't necessarily use the TV at the same time - it triggers an error. So if you want to see what's on the screen, you'll need to plug straight into the PSVR box.
If you just want to use PSVR by yourself in normal conditions and don't care about the social screen, though, it works great.
Need to test and see if you can work around the social screen issue by simply disabling deep color and HDR options since I think the signal mis-match is causing the issue (the PS4 is outputting 12-bit color which the PSVR box won't deal with).
Better than constantly shuffling cables around, at least.
The PSVR processing unit is really a piece of junk, though, and it's insanely disappointing that Sony would basically sell you a box that degrades picture quality on high-end displays while limiting the potential of PS4 Pro. They SELL high-end TVs and the Pro...and if a user has a PSVR, the quality of the video will be degraded. I can't even begin to understand how this happened but it's a big deal.