You're doing 40% water change every other day? That is actually too often. Do one 50% and one 100% each week. The water changes could be keeping him high-strung, too because they're too often and it stresses them out. Do you take him out each time? If you get a gravel vac, you can keep him in when you do the 50% change. Then you only have to take him out of the tank once a week.
I have one of my bettas in a 2.5 gallon, and I actually do two 75% changes with a gravel vac twice a week. So I don't have to take him out of the water at all. I don't check his water parameters super often, but when I do they're usually good. Buy a liquid test kit, too. In case the ammonia or nitrites gets too high in between changes then you can change more of the water more often.