A useful distinction
A modern dish inspired by a museum story can be an adaptation without reproducing a documented historical recipe. Claiming reconstruction would require evidence about ingredients, method and context. An attractive plate cannot supply that missing record.
Put it into practice
Explain which source inspired the idea and which choices are your own. Use a suitable tested recipe for practical preparation. Describe the result as an adaptation where appropriate, preserving the difference between a cultural reading and a demonstrated recreation of a particular historical dish.