Have you seen him actually biting his tail? I'm currently dealing with a tail biting HM, and I think he started because he didn't like that I was gone for a couple weeks. I would offer your fish different decorations or a change of scenery to see if he becomes distracted by that. Sometimes putting another betta by their tank will help them by distracting them, or other times it will stress them out.
If it is tail biting, you could also place a mirror by the tank for a little while every day to encourage his flaring, but not stress him out completely. He will see himself in the reflection and think it is another fish (unless you have a really smart cookie like my HM who won't perform for the mirror

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As far as tank size goes, he would probably appreciate the larger space. My HM is in a 2.5 currently, but no matter the size he still bites himself (he also did it in his .5g QT tank).