Memorizing the layouts altogether would be a step too far. And probably some people could do it...
I was thinking more of remembering that the layouts have basic characteristics: a team's words are not bunched on one side, or all lined up, or in a circle, etc. Not your team's, not the other team's.
But now that you mention it, fully randomized would be easy to do as a phone app. And a phone could be propped up in front of the spymasters. (The setup with the layout propped in front of the spymasters works really well in a party setting, where it's normal that some people will get up and walk around without wanting to cheat.)
I was thinking more of remembering that the layouts have basic characteristics: a team's words are not bunched on one side, or all lined up, or in a circle, etc. Not your team's, not the other team's.
But now that you mention it, fully randomized would be easy to do as a phone app. And a phone could be propped up in front of the spymasters. (The setup with the layout propped in front of the spymasters works really well in a party setting, where it's normal that some people will get up and walk around without wanting to cheat.)