My method is similar, except that once it boils, I stir the rice once and then simmer on medium high heat until the water level gets down to the surface of the rice and steam pockets (“rice eyes”) appear. Then reduce heat to lowest and cover for 20 min.
I’m going to try your fluffing method.
Also note I have made a mixture of multiple types of rice, same way, with no issue.
Honestly I only actually learnt the Asian method about 5 years ago and was kicking myself for not researching it earlier. It's so much better and insanely reliable across different types of rice.
Edit: after it is done I tend to take the lid off, stir it and let sit for a bit to let it air out. That helps a lot.