Well, I haven't done much on this for a while, but lately I've taken the time to do a bit of research.
It turns out that low oil pressure is pretty common on these engines and they do tend to tolerate it pretty well. The oil pressure port is tapped into the camshaft, so if everything is a bit worn there's a good chance all pressure has bled off before the port.
It's been suggested that I actually start the engine with the banjo bolt removed, rather than just cranking.
I think the next job will be removing the sump, checking the oil pump and bottom end clearances, though I'm thinking this will lead to a full rebuild anyway.
As for parts:
Standard bore rebuild kit ~$900
Rebuild kit upgrading to 85mm bore/2088cc ~$700.
Timing chain ~$50, or a kit with sprockets ~$200
Oil pump rebuild kit ~$100
Clutch kit ~$300
Wondering how much can be taken off the cylinder head. I'd like to be fairly conservative with this, but some extra compression would be nice. Stock compression is meant to be 5.77:1, but with a larger bore and a little bit taken off the head this might end up more like 6.5:1.