Update.
I've borrowed an 8-port HDMI splitter from work, which is overkill, and worked out why I'm getting odd behaviour when switching the BS4 into standby: it's because I'm powering the A/V tools off the USB on the BeoSystem which goes dead when the unit is in standby.
So to summarise, I'm an idiot 🙁
I've setup 4x BL17s and BL19 with the BS4 and am trialling it on the family this weekend. I still need a centre channel that I don't currently have, and am browsing eBay for a used 7.2 unless anyone has a better suggestion.
Having wired up an IR-eye with the correct cable, a final snag is my Beo4 is I believe too early for the BeoSystem: it lacks the navigation button. I can do everything from set the volume, display menus, and so on, but not go up and down the menu entries. I've had to steal the BeoRemote One from the Horizon.
The Stage has been decommissioned. I'd forgotten just how superior the sound is from a proper surround setup. The Stage is good, but it's good like a BeoSound 1, i.e. 'modern good' and no replacement for old fashioned separated sound.