Probably less "Drill Instructor" than "Training, Advising and Counselling Officer (TAC)" like Lt Chang in
Coming of Age http://memory-alpha.wikia.com/wiki/Chang_(TAC_Officer) or the Navy Counsellor (NC) rating (which has little in common with the Starfleet Counsellor, which would be a Corpsman/Hospitalman rating (HM) if they were involved in that at all, Starfleet Counsellors (who may be related to the older Ship's Psychiatrist billet) would be
officers in the Life Sciences/Medical Division.
Actually given that she was previously 2iC to a
Major (a rank that is the same paygrade as, and holds the same (or slightly greater depending on service) authority as a Lieutenant Commander, plus most of the other characters have either WO ranks (any service) or non-Naval ranks then I'd stay that that element - though confusing - does mostly work.
That said, some of the others
are wrong. The First Lieutenant and the Ship's Master
could be the same thing (tho I'd argue that if such an anchronistic post was to exist, it would be held by the CO or XO) or the First Lieutenant and the Security Chief, but all three being the same person is something of a conflict of interest IMO. The ChEng being CWO (if such a thing exists) or a senior Sgt or CPO if they don't makes sense (For instance, "Charge" the ChEng for the HMAS
Hammersley (a patrol boat with a crew of ~20) on the show
Sea Patrol was a CPO), however WO Boylan is the
Medic (ie a Corpsman/Hospitalman) not the CMO, those are
commissioned officers. Some of the others are questionable, but the only other ones that seems wrong are PVT Cook, who while he might be the primary
helmsman, would not be an Asst Navigator as that is a specialist function (either solo or merged) as we've discussed before; and SGM Paris who is listed as the SUPPO (tho he could be that as well) when he should actually be the Master-at-Arms/Security Chief/COB.