Aaron,
I don't fully understand the way you created those interaction regressors, but if those 7 tent weights for one interaction term shift one learning step for the next interaction term, those 7 interaction regressors are essentially collinear with each other, and it is no surprise to see those Z-values summing up to 0 in the end. In other words, if you put those 7 weights for each interaction term as a column in a 7X7 matrix, you will see all the numbers add up to 0 both horizontally and vertically, indicating collinearity.
Such a collinerity doesn't necessarily mean your approach is not appropriate. That's just some mathematical fact due to the way you created those regressors.
Gang
