In addition to Lamina Design, another one to check out is Pepakura Designer:
http://www.tamasoft.co.jp/pepakura-en/

It can take polygon data in a similar way as Lamina Design, looks like it supports OBJ, 3DS, LWO, and STL formats all of which are supported by MoI. I'd recommend trying OBJ format, but I'm not sure if it supports multi-sided polygons or not. You may need to adjust the option when you export from MoI, from Output: N-gons (which allows many-sided polygons in the generated OBJ file), to Output: Quads & Triangles (which only allows 3 or 4 sided polygons in the generated OBJ file).

- Michael