Interesting idea Daniel.
Actually I was recently thinking to myself if it were possible to invite other styles to the open embu portion of Shodokan tournaments.
Was thinking about testing the concept at my Aikido Festival later this year. Would make things interesting I think.
On another note I know that there have been Aikido styles that have competed in demonstration elements of Jujutsu or open style competitions and won as well. Saw it on ESPN some years ago though.