Is the Kula of Shulchan Melachim regarding Bishul Akum an objective list of ingredients or a subjective principle in regards to what I would experience as fitting for a king’s table?

Shulchan Melachim is not a Kula (leniency) but rather part of the definition of the prohibition. The prohibition of Bishul Nochri (gentile cooking) serves as a barrier to social intercourse that might lead to intermarriage and assimilation. Any food which would not be served at a meal to which one invited guests was not part of the decree. Apparently this rule would rely on local custom, and might change if a food was once not considered worthy of guests but is currently considered proper, or vice versa.