Show category selection below body on content editing form

Agaric has a fair amount of categorization going on, including some multiselect forms that take up a lot of room. We would prefer to have our CCK fields and node body field displayed first in the create content / edit node form, and the taxonomy choices below it. (I know better how to categorize something after I've written it, how about you?)

A quick search turns up nothing about rearranging this form, which means I must be using the wrong keywords.

I think however it can be done with my old, dear friend form_alter.

Resolution