So, I'm interested in recording my country turn-by-turn. Is there currently any way of doing that?

pen and paper =P

eestats, maybe?

find a good status tidy, and save the output with notes.

Most alliances have country boards you can save status tidy output to. However it is usually a snapshot of the country after running your turns for the day.

The notes can be for relevant events purchases, sales, bonuses, incoming/outgoing attacks, and country events like earthquakes and what not.

upload to boxcar, u can see history of your spyops from there..

or else

you can always take a screenshot of your advisor screen everyday/print it like what I did during the early 2000s

turn by turn? why not just day by day?