The missing media type is most likely due to a localisation decision with the Canon drivers - somewhat bizarrely, Canon include different media types in their US, European and other drivers.
I had similar issues with trying to profile BCs Optica One and Elegance Velvet papers on an iPF8300 some years ago, where the recommended media type was simply not available in Canon's UK printer driver. I sent a technical enquiry to BC, and their expert suggested an alternative media type which they assured me had a similar ink load and should produce good results.
I've always found BC very helpful and, as mearussi said, they will also make free custom profiles for their papers if necessary. Suggest you email them and see what they can come up with.