The message
from Dave contains these words:

Have you considered splitting the heating into zones with (say) a
separate timer/stat upstairs and downstairs? I did this and have been
surprised how well it works, despite having an open staircase.

Snap.

I put the re-zoning off for years because I thought the open staircase
would make it ineffectual.

FWIW I have a Danfoss TP75 downstairs (replacing an earlier Digistat
which itself replaced the stone age stat) and a Horstmann Centaurstat
(from Screwfix) upstairs ( which replaced an even cheaper and extremely
crappy programmable stat also from Screwfix).

The only complaint I have with the Centaurstat is that it has no holiday
setting. I got round this by inserting a switch in the call for heat
wire and rely on the downstairs heating only when I go away in winter.

--
Roger Chapman