"would render the country fairly useless till they’re all codified somewhere" Not really, almost all of the things done by government for the daily management

"would render the country fairly useless till they’re all codified somewhere" Not really, almost all of the things done by government for the daily management of the country are not related to the constitution and are already codified. You would need to figure out, agree and codify a mechanism for changing power, but you can arrange it so that you have years to do it and codifying that small part is not that huge of a task; USA had long conventions but that was more because of the need to actually create a country; and many other countries post-revolutions have functioned quite reasonably while codifying the constitutions, because it really doesn't affect the daily things, and you can run on interim rules (in UK's case, continuing as before for a limited time) until it's done.