I don't think there's any constitutional convention for holding a referendum. The broadest possible consensus must be sought. I understand your committee is trying to reach that consensus. That's what will be determined that at the end of the exercise. That's the first thing to consider.
The second thing to consider in terms of legitimacy is that in a representative democracy, the political parties that appear before the voters have democratic reform proposals in their political platforms. In a system of representative democracy, if we add up the political parties elected with the promise of modifying the electoral system, it also provides legitimacy to the process.