I earned the tumbleweed batch for what I think is a well-formulated question. Meanwhile I figured out the answer and posted it. But it didn't receive much attention; is Cross Validated a poor place for my question, or is it simply too specialised (which is not the same as too localised)?
http://stats.stackexchange.com/questions/108765/in-inverse-theory-how-do-i-transform-the-averaging-kernel-matrix-to-a-new-grid