Finicky Pets

When customers of mine at the store decide to make the right choice and feed their pets the “real stuff they need”, i.e. healthy nutrition, they often come back within a couple days telling me that their pet doesn’t like the new food.
My first reaction to this is always “that’s ok”. Just another indication that our pets, contrary to what we believed, not we, but they run the show. But seriously now, most of the less healthy commercial food is formulated and prepared with very strong smell and flavor so that pets will be attracted to it. Healthy food does not contain these flavors and cooked fats and other things. This may make it less appealing to the pets and they won't like it. Of course this is only an initial reaction and they will like it once they get used to what real food should smell like. The goal here is to feed them what's better for them in the long run. But how do you get to that point?
I always have two suggestions on hand:
Either take them off their old food with a sort of “cold turkey” approach. In other words, completely stop using the old food and exclusively switch to the new one. Feed them daily as suggested and also as they are used to. I.e. do not make changes to timing and frequency. Remove and discard what isn't eaten after 30 minutes even if means all of it (By the way, I consider removing uneaten portions after a certain shorter time period as good feeding practice). Clean the dish. In a day or two at the most they'll get hungry enough to eat it. And form there on forward will be no turning back.
Or, alternatively mix the new food with their current food starting with small, like 10% amounts and over time increase the ratio of the new food while decreasing the old one. Remove what is left after 30 minutes and clean the dish. This presumably lets them enjoy their current food while they become accustomed to the new stuff.
When pet owners hear of my first suggestion, they sometimes look at me like they want to say “You are cruel. You want to starve my pet?” That is silly. Our domesticated animals eat far more often than they would in the wild. A complete and disciplined introduction of healthy, real natural food and its removal after a set mealtime helps get them into a fasting and feasting rhythm like they would have if they had to hunt for their food. If they miss a few meals because they're being picky, it will NOT kill them. Quite contrary, they'll learn to appreciate their food that much more.
Regarding my experience with our own pets I have to report that either method worked for us. When the “humane” 2nd solution did not work, the first one always did the trick. After being in the pet food business now for a while and constantly dealing with different and new foods, the issue is no longer a subject in our house anyway. All 5 cats and 2 dogs eat what they are being presented when it is their meal time. None of them even thinks twice before digging in. And all of them are healthier and happier than ever before. It also proves, variety is the way to go.
I would be very much interested in hearing what tactics you used to make diet changes for your cat or dog. Always willing to learn I am anxious to see if there are more and possibly pet friendlier solutions to the task.