I'm only against using actual dates because we don't know the pace that our story will take. Canonically, Sandfall has a date system and major events in the world's timeline (such as the Revolution) have a specific date. If our goal is to eventually get to the Revolution, we don't know how long it will take for us to get there, so I think it would be easier to retcon in the dates.
Using "Day #" sounds good for me.
Using "Day #" sounds good for me.