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.

For a "couple of days a year" get a pedestal fan straight on everyone and leave the features in the ceiling. Seriously...I have 12 ceiling fans in my house and two wall mounted fans...the wall mounted fans are so much more effective then ceiling (and I don't know where you live, but did you know fans have a "summer" and "winter" setting??). Most people don't. Tip: turn the fan off before changing the setting.

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!

Just a thought, have you checked your lovely flooring will persist under new cabinets or more importantly the gap created by the island bench. Possibly put a simple narrow breakfast bar (with power point of course) across a couple of the window sections, lovely to sit and look out of the window and preserve the look and the light. Then you would save some depth into the living space, as the current breakfast bar is quite large and deep.