In the current situation I have time on my hands to try things, but only at home (hence the cramped pictures below, with garden toys in). An injury meant last year's trip didn't happen as planned, but I bought the tarp anyway. As I commented before, keeping the bike upright with guy ropes should work, and it does. Here they're attached to the drops. To protect the bar tape I'd use a small loop of webbing in the future as the cords dig in.
This position also makes loading and unloading the bike easy. The aero bars (bought since I asked the question) and phone mount are a significant reason to keep the bike upright. It's very stable. I can give the saddle or back wheel a good hard smack , or lift the back wheel to one side, and it's in no danger of falling.
Then I put a cheap lightweight 3m (10ft) tarp over the top. The aero bars form the apex of the tent. One corner is pegged down nearly 2 metres in front of the bike, and two are pegged down near the end of the guy ropes.
The 4th corner is pegged behind the bike with a short length of cord. The saddle and saddlebag are covered. The midpoints of the sides are pegged down, with cord if necessary. Unhitching the cord at the front centre of this photo allows easy access.
It's pretty spacious inside, and provides enough cover to get changed without offending anyone, unlike a tarp slung between trees. I'd be happy to use it on a campsite, which was one of my goals.
I had a comfortable night in there, admittedly in very benign weather. I pitched it with the bike facing into the slight breeze, so the upwind end of the tarp was pegged to the ground. In this orientation, using a length of cord to prevent flapping fabric, it would be possible to shelter from the elements while cooking on a small stove (another project) just outside.
A tip from a friend - sleep on the non-drive side, in case your sleeping bag brushes up against the bike. That said you could actually fit a short person on the other side of the bike
And this is it on Dartmoor a few months later. I pitched in the dark and fog after a day that was hillier (i.e. slower, also with a record 3 punctures) and much wetter than expected. It did a good job of keeping the rain off but the fog made everything damp. Various lessons have been learned about what to pack where for accessibility, and I need to pick a bigger spot next time (the tarp only extended onto the path while I cooked breakfast under it, but still it was a bit tight). One change was fitting the guy ropes to the aero-bar armrests, which was easier with my bar bag fitted. One thing I might consider is protecting the tarp from the strain caused by the aerobars, perhaps just by using one of my existing bags.