This travel guide site https://gurutabi.gnavi.co.jp/i/gm101/ have a collection of 1918 entries about meibutsu meals from different area all around Japan sorted by popularity.
Most entries have info about the food in Japanese including area that the food is famous in and time that the food is suitable to be consumed. Most of them also include a short summary. But there are little info about when it start become popular unless it's describe in the summary.
And then, Rurubu the famous Japanese travel guide publisher have also selected ~250 such meals on their website http://www.rurubu.com/season/special/gourmet/ . While this site have less entry than the previous one, they're probably more carefullu selected, and there are also link to list of shops that supply each of those foods together with relevant map and contact method and such.
Or, perhaps another way to look at it is to look at what each town is offering to supporters in the Furusato tax campaign: https://www.furusato-tax.jp