All the SDKs I’ve found (Google Play, ScoreLoop, Skiller) are based on the use case: “submit score and we’ll check if it is higher than the previous one, reacting accordingly”.
I need something more along the lines of “submit score and we’ll automatically add it up to your previous score”.
Can anyone recommend an Android SDK that works in that way, or one that can be adapted to work in a cumulative way?
Yes, that’s a possibility. The only drawback is the incoherency that will happen in the daily and weekly leaderboards which cannot be manipulated manually. Only the all-time scores will make sense.