So, are there any other options? Enter the Recruitment Duty Officer Missions.
While not as convenient as Reassigning Under-performing Officers, there are two specific types of Recruitment assignments you want to keep an eye out for:
Both of these will allow you to trade existing Duty Officers for a chance at an equal or better one. Unfortunately, there is a chance for Disaster on both of them. Disaster on Asylum assignments means the potential officer simply backs out. However, with Officer Exchanges, you are at least guaranteed a Common officer, which isn't bad as far as disasters go.
Each assignment will be related to a different species, so what they'll want in order to increase your odds will vary from mission to mission. Asylum assignments do require that the DOFF used be a Refugee, but unfortunately their listing on STOwiki seems a bit incomplete at the moment (which is understandable). You can buy them on the Exchange, although that does mean they'll be subject to the ups, downs, and manipulations of the market. I personally expect them to become more valuable as time goes on, but that's just speculation.
As a result, flying around various sectors, looking for these missions, would be rather worthwhile. As an added bonus, you'll be earning Recruitment Commendation XP when doing them. This will get your nicer Duty Officers in time, and once you hit level 4, then you can turn in the Commendation XP for Fleet Marks. Asylum assignments take 8 hours to complete, with Exchanges taking 4 hours. Both would make reasonable lunch-break or log-off activities in my opinion.