So no you have a situation where the government can have split brain: some parts of the legislative branch can be party A and other parts can be party B and the president isn’t tied to either.
From what I understand when the US “brings democracy” to another country we set up a parliamentary system and that system is widely seen as better. You cannot form an ineffective government by definition, though you can have a non-functioning government that is trying to form a coalition. These types of systems tend to find center because forming a coalition always requires some level of compromise. Our system oscillates between three states: party A does what they want, party B does what they want, and split brain and president does what he wants because Congress has no will to keep him accountable.
What I would like to try is a combination of parliamentary system, approval voting, and possibly major legislation passed by randomly selecting a jury of citizens and showing the the pros and cons of a bill. If you cannot convince 1000 random citizens that we should go to war, maybe it’s not a good idea.