In my opinion the only way Mominul will improve is if he is with the national team. Doesnt have to be in the playing XI but around the camp he should be given attention by coaches and he will learn to develop good temperament. And also Anamul/Mominul have played together so much its best with they also learn together in the national team.
We could give Nafees Iqbal a go since we dont have standout candidates. But that all depends on if Anamul will open in tests or bat at #3.