There's no reason for PS3 to have a problem with it. From a PS3 or PS4 standpoint, it would simply be another save game file. All PS3 and PS4 games can (if their developers choose to use the feature) create as many save game files as desired, and most let you create a new save any time you want.
The console versions of FFXIV already use two different types of save game files, one for your account-wide settings and another for the hotbar/gearset/macro/etc settings for each of your characters. This would be a third type, but unlike the other two could be saved and loaded on command with an interface similar to what most single player games use. It would create a file when you choose to save your HUD settings and when you choose to load from a saved HUD file would ask you to select one and would overwrite your HUD with what's stored there (leaving everything else alone except for the HUD settings the feature stores).