For what it's worth, Franz Joseph Schnaubelt's Star Fleet Technical Manual
discusses bearings and headings and has a system that instead of having 360 degrees in a circle has 400 "divisions." (See Technical Order TO:02:06:10.) It also has "centidivisions" and "millidivisions" instead of minutes and seconds. So at least the old Technical Manual
would seem to contemplate a heading of something like "375 mark 382." (Schnaubelt uses a small superscript "D" instead of the regular degree symbol of a little superscript circle.) Of course even this "400 'divisions' in a circle" notion doesn't really account for dialog in TOS
with bearings and headings in the 800s and 900s.
But it's possible that if Schnaubelt's ship names and ship designs from his Technical Manual
(like the Destroyer Class U.S.S Azreal
NCC-517) are being adopted for the production, it's possible that his bearing and heading methodology is also being adopted as well. I know the old Technical Manual
has many adherents who think that if one page of it was shown briefly on a computer monitor in The Wrath of Khan
, then the whole darned book must be canon as well.