Mine works again.
I did the same thing some one else did; went to the Delta Volanis Cluster, got the mission from Lieutenant Grall, went into a system, and I could slot Bridge Officers again.
I think that the problem has something to do with either:
A) getting a new ship (I got 2 right before)
B) the anniversary mission (the Ambassador was one of said ships)
C)The Doomsday Device mission (I had just finished the first part)
D) All of the above
I have seen other posts from people who also did these things and got the bug, and I did them all.