I use the 301 trick on one of my websites and am seeing great improvement, it jumped to #3 yesterday, another website jumped to #2. I still use H1 H2 H3 and co.. But i use LSI keywords too. With a 500-600 words article i don't use my keyword more then 5 times (h1, h2, h3, bolded on first paragraph, italic on last one and i underline my H3 to avoid using the keyword again). Also with low density the article will be more enjoyable and less spammy.
I am not waiting for you or the OP to show me if it's wrong or not. I know it from my experience.