They're gonna need someone to wake up the 1922 committee and get them to change all the rules first.
And this, kids, is why you ask experienced TTRPG system designers like me to draw up your political game system rules...
While TTPRPGs are a good source, I'd recommend the board game Cosmic Encounter as an even better source for political game system rules.
Among other things, it included a "Filch" card that let you steal cards from the deck when other players are distracted. (Later versions may have nerfed it.)
How many of the last 1922 executive have been returned? Is there enough of them to know the rules, change the rules and then run the contest or are they all in the dark now the Graham Brady isn't there?
Weeeelll this is where it probably ALSO gets fun. But we don't really know the rules of the 1922 committee. So god knows that their rules are on being quorate etc.
And yes, they may well need to run a 1922 election before they can even change any other rules.