Every time I bake something in a loaf pan, the centre doesn’t cook and the loaf sinks - badly.   The edges are well cooked.  This happens on more than one recipe: Lemon Loaf, Banana Loaf, etc.  But  items that I bake in round or rectangular cake pans turn out fine. The attached image is the worst example. I’ve checked the following: -ingredients like eggs, milk, etc are not cold from fridge. -baking powder and baking soda work well in other recipes, so are not expired. -oven temperature is spot on, verified digitally I’ve tried:  reducing oven temp 25 degrees F (eg from 350 F to 325 F)  I even tried 300F! adding more flour to make thicker batter putting foil around outside of loaf pan to reflect heat. adding an extra egg yolk. reducing balking powder (or baking soda depending on recipe..) using full fat dairy, (eg sour cream or milk, etc) instead of "lite" baking for a longer time so that centre finally sets.  In this case, the outside of the loaf cake overcooks and is hard as a rock.  The loaf pans are from Baker’s Secret, and although the pans are dark, I’m sure thousands of people around the world use these pans.  Besides, I did try one experiment in which I lined the outside of the pan with aluminum foil - no difference Any suggestions appreciated It seesm to happn on any loaf pan recipe.  Here's an example that sunk:  Bon Appetit's Best Banana Bread 
I think you were absolutely on the right path - what you need is a lower temperature for a longer time. Many of your observations in your answer point in that direction - the liquid core, the fact that the crust overbakes when you bake longer, and the fact that the same recipe works well in a flatter shape (in a rectangular pan), where the heat reaches the core quicker. You wrote that you have already tried it - it just seems that you didn't go far enough. Temperature is just a number, you have to change the temperature until the results are good, not the other way round. The other thing you can consider is turning off any convection function, if you have one. It will bake slower, but more evenly. 