A ha! Okay, so I just tried with GAM -- because that's how I calculated my betas, contrasts, and everything else -- and perhaps unsurprisingly, the response functions are all the same shape (modulo vertical scaling).
It would seem the "one parameter" is the scale factor, but then why solve for both beta and scaling? Or is it that the response functions I'm seeing are a zero-parameter GAM (since I didn't explicitly parameterize it) scaled by the betas?
In any case, I'm trying with SPMG3 now, since our original goal was to get outputs similar to what SPM used to give (which was before my time).
Thanks much!
Aditya