If the South Beach prepackaged foods have soy listed in their first ingredients, then there is enough soy in the meal to make a change in your INR if you are eating them daily. I know I have had to be very careful that the protein shakes I buy are whey and not soy, as well as any bars. The South Beach diet itself isn't a soy-rich diet when you prepare your own meals. I'm sure they use soy in their prepackaged foods because it contains less fat and allows them to keep the fat grams down while keeping the protein component up.
Kristy is right, if it's a diet that he will be consistant with, then the dose can be adjusted accordingly. I don't eliminate Vitamin K containing foods. I also eat edema on occasion (love it raw! shelling it like peanuts - mmmm) but something that is made from soy flour or a processed soy, is going to contain much more K than edema. Much like it's better to eat the fruit, than drink a cup of the juice you get from it. Orange juice (because it take a lot of fruit to make a cup of juice) contains much more sugar than just eating the orange.
Terry, I think your husband is having his low INR from a few factors. It sounds like he's begun his "get healthy" plan all at once, so the soy product and the exercise are both playing a part. I started exercising regularly a few years ago. I experienced a drop in my INR, but not a severe drop. I just get the feeling that the soy protein (because it's in concentrated form) is the bigger culprit.
And all that being said - Ross has a point. He most likely should have seen a change in his INR with a 20% increase. But I will say that when I had my protein bar debacle that was causing my low INR, we were raising my dose regularly and my INR was not moving and didn't move until I figured out it was the bars causing it and I stopped eating them.