You didn't discover a 2' height difference between the two rooms until after the demo? Design starts long before demo and it starts with measurements and creative problem solving. An open concept does not work in every home, as you are unfortunately discovering. I suggest adding back in a wide cased opening between the rooms. It will still be plenty open.

Before the demo, there was a large decorative arch covering the height difference. The initial thought was the kitchen ceiling could be raised to the height of the living room.

Here is a pic before the arch was removed

IMO 10' ceilings are the max for both heating and cooling $$$$ saved not to mention the sound and how it is affected by those high ceilings that really serve no purpose. I think there are many things in old houses that are not obvious until demolition. I agree to lower the ceing to do all 10' ones and in the kitchen take the cabinets to the ceiling and save on heating and cooling If you want the higher ceilinng then the work around is live with the difference.

Varied ceiling heights make for a more visually interesting space. If you've lived with the 12 foot ceiling in the living room and enjoyed it (and didn't worry about a miniscule rise in your heating bills), then why waste money by dropping the ceiling in the living room to make all the ceiling heights the same. The open concept you want will not be negatively affected by the different heights, and as I said the space will be more interesting.