The upside of a quest that uses regular items is it is always really fast to complete. Anyone can grow in advance and even cook in advance. Just store your dishes in your fridge til Quest time and then serve them up once Thursday comes.
I do want to give a small warning this quest is a HIGH dish count quest. IE You have to cook 149 of EACH dish.
So lets look at our dishes.
Lingonberries are in the fruit section, down toward the bottom, Pine nuts are in the grain section down almost to the bottom and Puffin are in exotic animals at the VERY bottom.
Mantis Shrimp are in Crustaceans, at the bottom of course. Mushrooms can be found in salad and beans, in the middle of the first column. Tomatillos are nice and easy. They are at the top of the exotic vegetables. And if you were around during St pats or Rock the Ranch you might have a few of these lying around.
Third Dish. This is gonna be the one that gives everyone a headache. Two ingredients over 12 hour grow times and the cook time is 18 hours as well. UGH.
There is no spreadsheet of course for this quest since there are no seasonals. I just want to reiterate that you need to have 149 of each dish. SO for the 3rd dish ALONE you want to figure on at least 50 or so hours of cooking assuming you have the maximum 53 stoves. IF you have more stoves or red stoves this will obviously go quicker for you. I know I see in groups and in chat a lot people waiting til the very last minute on quest dishes some times. You can't do that here. (You shouldn't do that at all actually but I digress). Unlike seasonal dishes there is no added bonus to cooking extra. So most people will not have extra dishes on hand. Although I do believe ingredients will be plentiful even early on in the quest.
Good luck and Happy Ranching!