That's what the King/Queen is for.If given any significant power (which, unless we want to play a declining power, we are almost certainly going to do), whether equal or unequal, our Upper and Lower Houses are going to disagree to the point of gridlock. When it happens, we'll need to do another constitutional convention to resolve the issue. Hoping that we can avoid it by waiting 25-50 years seems much more expensive than dealing with it when the time comes.
One-off situations, he/she intervenes.
When it begins to seem systemic, he can call another ConCon.