You asked about this specific ceiling. Combined with all that's going on in that room, that ceiling goes too far for me and that's saying a lot. I do love the look of a decorated ceiling and this one could have been spectacular without all of the action going on under it.

If the roof in the sunroom is also flat on the exterior part of the roof then perhaps put triangular windows in the top part of the wall that would look straight outside and then keep the sunroom ceiling flat. You wont notice its different as the window to the outside will be the feature of that wall.

You never mentioned your budget that you're willing to spend. You could add a thicker fill backed insulation blanket - 50mm, 75mm or 100mm are the common thicknesses. Steep roof pitch so would need scaffolding, harnesses, etc.. which adds up quickly. Probably still not enough insulation though but probably cheapest option. Insulation under existing timber linings then reline over the top of that as some have suggested. Working at height though so would need scaffold set up again and working overhead is not fun nor easy. You could replace the roof with a sandwich panel roof. Try Versiclad or Kingspan or comparable. They have a polystyrene type of insulation between an outer metal roof sheet and a metal inner sheet. These are heat laminated together. Again different thickness available from 50mm up to 180mm is common. The 180mm has a R rating of 4.7 which is quite good. Again steep pitch, etc., probably need new ridge capping, etc.. Probably most expensive option...... Keep us all posted on your decision though!

The lounge in our 1956 house in South Africa had a stained wooden ceiling. The house didn't have any insulation so the lounge would become really hot in Summer. We opted to have the original ceiling removed and dropped 150mm so we could install insulation. We needed to paint the original panels but left the varnished beams. Every wall in the house was painted white, which I found too stark. I decided to paint the lounge using a light blue and a peach colour. People thought this was a bit bold, but I was happy with my choice. The before photos were scans from the 1980s, as I couldn't find the original EA photos when we bought the house.