So from the rules, I gather that this plays more like Resistance than Mafia. I think that we should carefully manage who (potentially) becomes president in the same way you need to manage who proposes a mission in Resistance. Unlike Resistance we don't have to accept any of the three proposals, but that comes at the cost of a (likely) fascist law, so we don't want to do this except in extreme cases.
Hence, we should accept one of gkrieg, Archetype, or Tables proposals. As I am a potential president in the 2nd turn if gkrieg is not elected, I will reject the first government unless I would be chancellor.
Currently, I think that the president is the more important role. While the chancellor ultimately decides which policy is enacted the president can discard a liberal law and claim that he didn't draw any.
What do people think about revealing the drawn cards. I think it is in our best interest that the president and the chancellor claim what cards they drew so that we can card count. Obviously, either of them could lie, but perhaps one can deduce a fascist from that...
One thing, I'd like to propose is shadow cabinets. The idea is that all of the potential president candidates suggest which chancellor they would appoint if it came to them. So we get some information out of the later players even if we accept an earlier government. Perhaps this makes only sense after gkrieg's proposal when we have some information. Obviously there is no rule that forces a player to actually appoint the chancellor that one had in one's shadow cabinet, but that would demand some scrutiny.
One final point: What do you think about the strategy for the president in the 2L1F case. In my opinion one should pass both liberal laws to guarantee a success over passing 1L1F and letting the chancellor decide.