I do not now why it is an issue for you but that is what we are trying to work out. I certainly have no problem on my test site making this work as expected so it is not a general problem.
Let’s just go back to the beginning because I see you have not really followed our advice so far.
First you have two moderators. BOTH are in more than one user group. One is in 2 groups and the other in 3 groups. Just to keep things clean and tidy I would repeat my recommendation to limit these two users to just true moderators group.
Next – I see that all of the edit permissions for the ‘moderator access’ permission set are turned on. We did recommend that these should be limited to those you really want. Of the three ‘post’ editing permissions choose the one you want. Now I must ask say that it works for me without doing that but keep it clean and simple and give it a try.
If we can get past these two tests which we have been urging you to do and things are still not right then we can look elsewhere but this does have to be done one step at a time.