I wouldn’t worry too much about the stardates. The whole passage of time in the group is abstract anyway. We have a way to work out stardates based on the real date, but that is just for convienice and reference. Without the frame of reference, they really are just numbers that can mean anything we like. The real date just gives us a set of numbers to draw from.
08/12/2015 (DD/MM/YYYY format) = 81215.2236
28/05/2015 = 28515.2236
02/07/2015 = 2715.2236
10/04/2015 = 10415.2236
Taken in isolation, the only bit that really is relevant is the .2236 on the end as it denotes what the USFP year is.
We could come up with a different term for hours if needed, e.g shifts, phases, cycles. We are working in space, so I can see day and night cycles being in effect and then talking in fractions of a cycle or something, e.g. first quarter etc. Hours days weeks months and years is very much bound to our own planet. Would the species you have created use the same concepts? How would an aquatic species measure the passage of time? What of their world spins differently on its axis… would there be night and day? What then would be a more universal measure of time for all species?