I'm just spitballing on this... haven't thought any of it through yet, but let's see about this:
If we chose to make a substitution for Duo-Dimension it could be a Supernatural ability to Impersonate Artwork. Allow the Artist Genie to use a transformation spell with a Craft, Performance, or Profession check... that check then works as Disguise or Hide check providing the skill is suitable as a singer or poet couldn't really impersonate a poem or a song.
Sculptors could temporarily transform into statues or a relief to blend in with similar works, a painter could transform into a framed canvas and appear to be a portrait of himself, and so on.
Allow the effect to last as long as one round per Caster Level. Perhaps the ability is limited to changing the Artist Genie into something of the same size or up to one size smaller. Maybe the Artist Genie is considered Prone until he resumes his natural form.
If we chose to make a substitution for Duo-Dimension it could be a Supernatural ability to Impersonate Artwork. Allow the Artist Genie to use a transformation spell with a Craft, Performance, or Profession check... that check then works as Disguise or Hide check providing the skill is suitable as a singer or poet couldn't really impersonate a poem or a song.
Sculptors could temporarily transform into statues or a relief to blend in with similar works, a painter could transform into a framed canvas and appear to be a portrait of himself, and so on.
Allow the effect to last as long as one round per Caster Level. Perhaps the ability is limited to changing the Artist Genie into something of the same size or up to one size smaller. Maybe the Artist Genie is considered Prone until he resumes his natural form.