Improving weapon specialty (gaining stars) in Breakdown mode

In State Of Decay YOSE Breakdown Mode: I know that you can choose to unlock a weapon specialty of your choice after reaching level 4 fighting/shooting.

So I have these random characters from the very first level (I am now in level 10) and non of them were all-star weapon specialty (They had no specialty). They were random characters or heroes without any stars.

Based on what I read about improving a weapon specialty, I decided to stay on each level longer & longer and:

1. I kept the same 6 characters alive and did not lose/remove/leave behind/expel any of them up to now.
2. I planned and choose a weapon for each of them to be specialized in it and never changed the plan. (For example: for the soldier, edged weapon; for the student, blunt weapon; etc. and all of them were maxed to 7 in level 3)
3. As I said I try to stay on each level long enough and on average, I have killed at least +1000 or +1500 zombies in each level.
4. I have upgraded Watchtower to Shooting platform and that Fitness area to the max so that I was able to use "XP Bonus for Combat/Shooting" in these buildings.

So, after all these, why has not even ONE star been added to any of my characters' specialty?! How many zombies should I kill? One million? What am I missing here?