I really think you're exaggerating the situation. The game in its current state isn't terribly exciting but it's hardly reached the level of absolute tedium. If we want to make it more interesting, the only thing we can do is try and increase activity, and I don't see what a new constitution has to offer on that front. Even if a parliamentary system were a likely outcome of a constitutional convention, how would that increase activity or make the game more interesting? If you want to reboot the legislative statute that's one thing, but a constitutional convention isn't really a necessary or efficient way of accomplishing that aim.
Since 2009, when that convention was crashing and burning, I have made the case that primary means of increasing activity must necessarily be a bottom up process and attempts to legislate or reform it into existance will surely fail. Switching systems is a trade-off, functional improvements are just that and "Stirring things up" only lasts a short while whereas the traded-off consequences could be long lasting.