Hey @ffaubert!
Being able to easily access displayed data is something the dev team is working on but there currently isn't a timetable and they're considering a number of different implementations based on people's requests.
It may also be possible to build out a better workaround with the new table's API, especially as more features get added to it, but for the moment the best I know of is to use a manual JS sort. What discrepancies were you seeing when you tried to do so?
A similar question of being able to access sorted data in a filtered table came up here.