Hmmm... fighting (as in a story going from fight to fight), or fighting tournaments/contests/series duals?
In any case, the above AA threads would have been among the first off top of head.
Another to have occured would be Ranma/Dead or Alive. But the main one I can think of ('Doaran' by IronRaptr9241) has only a prologue rewrite on FF.NET, and the rest (some 7 chapters worth) was removed.
Ranma/City of Heros crossover
R-COH 'A Hero's Awakening' by Agnostics Puppet - [Status=Not Complete] - [Last Dld=10/18/2007] - [Size=216kb]
Ranma/Highlander crossover
R-HGH 'Till Death Do We Part' by Dark Phoneix - [Status=Not Complete] - [Last Dld=01/08/2003] - [Size=79kb]
The 3 Ranma/History Strongest Disiple Kenichi crossovers I'm aware of are disqualified, all 3 on size, and 2 on quality.
Not exactly tournament, but Ranma King of Fighters
R-KOF 'Aerial Ranma' by screaming dean - [Status=Not Complete] - [Last Dld=01/03/2009] - [Size=499kb]
claihm solais has a two arc series called 'For the Sake of the Art' and 'The Longest Journey', the 2nd arc has a fighting tournament style in it.
Would Ranma/Revolutionary Girl Utena crosses count? Most are too small, but two would be over the size minimum.
There is some tournament style fighting bits in R-NEGIMA 'Ranma x Negima-Ranma's White Wings' by Dreamingfox. But it is not what you traditionally consider a fighting anime.
Also not a tournament style anime, but Ranma/Tenchi Muyo story called 'Lost and found' by Law-kun has Ranma and Tenchi at a tournament, in fact, a couple others do as well.
There is also at least one Ranma/DBZ cross to come to mind with fighting contests.
Hope at least some of that helps.