Maybe, I am not ready to answer one way or another.
If you look at the the money to install all this equipment, the the money you will spend running them all, you could have bought new glass to knock down that radiant heat gain in the first place. Your plan is still a patch, you seem to be blind by it's complexity, cost and design to justify the money it will take to install.
If you had a two zone system conditioning the home now, one system for upstairs bedrooms and one for the downstairs living area. During the day you are not in the bedrooms, this is when the kitchen is hot. Take a supply duct from that system and installing the kitchen. This will work fine all day long. Then at night, when the heat gain is non existent in the kitchen the motorized damper will close directing the air back to the bedroom where it's needed.
You are doing a lot of work for a very small kitchen.