Intuitive Eating is one hundred percent in line with taking great care of your health. There is no conflict there.
The whole notion of doing intuitive eating "right" is diet thinking. There is no wrong way to trust your intuition and take great care of yourself. That looks different for everyone. If your body is communicating that it isn't healthy, listen to it! Things go wrong when we don't listen, not when we do. There is a whole chapter in Intuitive Eating on gentle nutrition that should give you some ideas on how to balance fun and satisfaction with good health. There is no requirement that you eat a whole lot of something that hurts you. The way to avoid any kind of pendulum swinging is to leave WEIGHT out of it, along with guilt and fear. Don't underfeed yourself or place anything completely off limits. Don't tell yourself scary stories about failing and doing it wrong. Eat whatever makes you feel healthy and well that also tastes good and satisfies. If you notice a food you love is causing problems for you, have it less often, in smaller portions, at a different time of day, with a different combination of foods, or seek out a tastier replacement. There is always a way to totally enjoy a meal and feel great afterward. Look at it like you're conducting research or detective work on maximum satisfaction, health, and enjoyment. This is a fun puzzle to be solved, with lots to be learned and plenty of delicious food to be eaten.
That's how I approached it when my husband and I changed our eating for health reasons. I've written quite a bit about the mashup of happy and healthy eating in my own journal. Another really powerful element is fully owning whatever choices you make. As long as you are always free to choose, there is nothing to rebel against.
It's never an all-or-nothing proposition where you either go back to a restrictive diet mindset or you ignore your blood sugar until a limb falls off. There is a vast middle ground between the two just waiting to be explored.