Yeah it's a little conspiratorial but I honestly don't think Kojima is working on DS2.
With the directors cut he got to introduce all the features he supposedly wanted in a game like this. What would a DS2 include that isn't already in that? It feels like a totally complete game that absolutely doesn't need a sequel, and Kojima himself in the past as talked about how he doesn't like doing squeals (he never wanted to do MGS2 or any of the subsequent games).
I think Overdose is whatever he's working on next with Sony, either exclusive or multiplatform, and will have Reedus and Margaret Qualley. Maybe it could initially be DS related (bait and switch type thing) and then turn subversive like he did with MGS2 from MGS2, but as a straight squeal? I honestly can't see it.
The team isn't even big enough to work on 3 games. Overdose clearly isn't the MS cloud game, so those are already two separate projects, throw in DS2 and it'd be too much on his plate.