The distinction you are drawing is exactly the right one, and it maps onto a real split in who cooks this food.
Themed restaurants sell an evening. The menu is modern food with old names, and the research budget went into the building. Fine as entertainment, useless for your purpose.
Historical reenactment groups are the opposite. Many of them take period cookery seriously, work from surviving manuscripts, and argue at length about ingredient substitutions. The food is the point rather than the backdrop, and it is usually far closer to the sources than anything commercial.
The practical consequence is that your best route is often not a restaurant at all. Look for reenactment societies, living history museums with working kitchens, and open days at castles and abbeys where the kitchen is part of the exhibit rather than the gift shop.