Comment 82 for bug 179988

Some more things to try:

Try adding some code after the cairo_t* is created and before the Inkscape drawing code is called to draw a rectangle of a known size and check what size it prints out as.
 eg

cairo_set_source_rgb (cr, 0, 0, 0);
cairo_rectangle (cr, 2*72, 2*72, 4*72, 4*72);
cairo_stroke (cr);

This should stroke a black square 4" x 4" in size and offset 2" from the top and left sides.

You could also redirect the drawing to a PS or PDF file. eg

cairo_surface_t *surface;
cairo_t *cr;

surface = cairo_pdf_surface_create ("filename.pdf", 595, 842);
cr = cairo_create (surface);

and check if that works.