Eva Broman spotted this site and wrote to the Jewish-Music mailing list:
Just by chance I came across this blog with some wonderful pioutim by the Tunisian hazzan (Cantor) Acher Mizrachi:
Check out "Habibi Ya Habibi" with Itzik Kalah, achermizrahi.centerblog.net/4475505-Habibi-Ya-Habibi-Itzik-Kala
"Naguila Hallelouia" with Ruby Chen, il.youtube.com/watch?v=bPXb_XJLyQY
And a modern version with Stalos and Oren Chen, il.youtube.com/watch?v=vFGkbe4Gywc
Another Tunisian piout with Beni Barda, il.youtube.com/watch?v=LzdDA7gkt18
There is a lot more on the achermizrachi site. Here is an article about his music: Creative Cultural Fusions: "Orientalizing" the Ballad Melody, by Samuel G. Armistead, Faculty Research Lecture, 1998, University of California, Davis. Enjoy!