Match parallel camera to object

I’m trying to create a movie rendering (from an animated Bongo model) in parallel projected top view of an exact area of my model, in such a way that the rendered output matches exactly the boundaries of a rectangular surface in the horizontal plane. I can insert the exact dimensions in the render setup (pixel dimensions), but I don’t seem to find a way to match the safe frame exactly to the geometry I need to render.
So far I have been looking into showing the top view cam and trying to match it to the surface from there, but without any success. I also tried setting the viewport aspect ratio to match that of the surface, and use zoom and pan, but I find this insufficiently accurate (since the rendered output is needed for a projection mapping project with different superimposed layers).
Of course I could do some video editing in post production, but I’m trying to keep an as simple workflow as possible.
Would there be a way to render a specific area in parallel projection from coordinates input? So far I have only looked into the Rhino renderer, I could also give it a try with Enscape.