I have to say that I simply do not understand your post at all. I think of these things in terms of linear algebra and subspaces and projections. I don't understand the following sentences, for example:
"If I were to simply pass this to 3dDeconvolve, my understanding is that the SVD would "clump" my N regressors the orthogonal N-1 regressors that explain all of the variance in the original N."
"My belief was that the SVD is multiplying the data by a contrast matrix of sorts, running the GLM for the product of the X matrix and the contrast matrix, and then dividing the beta vector by the inverse of the contrast matrix."
You can use the 1dsvd program to compute the SVD and pseudo-inverse of the regression matrix, if you want to see what those are. The pseudo-inverse is what 3dDeconvolve uses to compute the betas from the data.
