I like the concept, but it seems like combat is only one pillar of 5e characters, and their abilities in the other pillars aren't going to reflected in the DramaSystem character. A high-Charisma bard with various social spells won't have any chance to cast them. Being trained in social skills won't help nor hinder in the Drama, but is an opportunity cost for taking combat-related skills. Or is the idea these would use used in the DramaSystem periods? If so, are they resolved with standard D&D mechanics (saves, etc?) or DramaSystem mechanics (votes, procedural resolution).
DramaSystem defines PCs in terms of having the relationship and what you want between the other PCs, but with the PCs being on the same team I see a lot of could be between PCs and NPCs/Recurring Characters, WWE style. You don't define these in character creation, and solo- or few- PC scenes may leave other players without things to do.
Finally, the rewards and consequences structure between the two games is kept divorced, furthering the split that these aren't quite the same realities.
It looks like you're playing two games interleaved, each with one vision of the character drawn in the style of that game. How do we bring them together so we can leverage 5e's social and RP pillar while taking advantage of all we can get from DramaSystem. And make the different scenes all meaningful, instead of DS only for DS scenes and D&D only during D&D scenes.
