Strategic data transfers (Courier) did seem to have an effect in my previous tests. I'll keep an eye out for some more conflicts to continue testing in.Some interim results. I went for lower faction wars that were a draw at 0/0 days won after 2-3 days. All missions mentioned war in the title and flavour text. In the Codex session log they all had War in the mission-type name. No further changes to the scores happened on the day after my test.
Missions that had no effect:
1x Surface recovery of 4 nerve agents
1x Surface recovery hostages
2x Deliver war supplies (weapons and Armour)
Missions that had an effect:
1x Assassinate Deserter
1x Assassinate Deserter + 1x Assassinate Venerable General
Some questions for further testing:
Maybe it is only combat missions.
Maybe the non-combat war-themed missions have less effect and doing more of them on one day would produce a result.