Harmony seems to take a much more active involvement in Scadrial than, say, Endowment or Cultivation do. He's got agents that move among the people, he plans out their technological and cultural development, and he intervenes through Marsh, Wax or TenSoon where necessary. If Bavadin were to go after anyone I'd expect it to be Harmony.
As for how much he's willing to invest, that's why I think he's teaming up with Bavadin - alone, he's going to get smashed. But Ruin has a part of his power lost in atium, and Preservation has fragments of his power within every human on Scadrial...which gives Odium and Autonomy the leeway to spend a few fragments of their power to create god metals.