I had fusarium problems for three years. I did a number of things; not everyone approves of my approach but I have not had the problem since. This isn't meant as a plug of products but advice. Some people have said this hasn't worked.
1- I used SoilGuard (check Gardens Alive catalog) which supposedly stops the fusarium from entering the roots.
2- I stopped using any of the varieties that really succumbed to the disease, which included Caspian Pink, Anna Russian, Pink Ping Pong, and others whose names aren't occurring to me right now. You can't totally go by whether the variety is listed as being F resistant - as I'm sure you know, most heirlooms haven't been challenge-tested for resistance. Varieties that have fared well for me include Rutgers, most potato-leaved varieties, Sungold, Black Cherry, Eva Purple Ball, Lemon Boy, Sanibel, Green Zebra, Jetsetter.
3- I've also used some grass mulch. I hadn't used that approach prior to the problem.
Good luck!