Hi Greyfox, thanks for looking into, however searching through the .xml file the profile you've found above is for the Mark 1 lens not the Mark 2. It seems that the xml has the following profiles:
For the Mark 1 lens:
<maker>Canon</maker>
<model>Canon EF 100-400mm f/4.5-5.6L IS USM</model>
<mount>Canon EF</mount>
<!-- Average crop factor of Canon APS-C cameras -->
<cropfactor>1.611</cropfactor>
<maker>Canon</maker>
<model>Canon EF 100-400mm f/4.5-5.6L IS USM</model>
<mount>Canon EF</mount>
<cropfactor>1</cropfactor>
For the Mark 2 lens:
<maker>Canon</maker>
<model>Canon EF 100-400mm f/4.5-5.6L IS II USM</model>
<mount>Canon EF</mount>
<cropfactor>1.613</cropfactor>
And that's it, so nothing for the Mark 2 lens on a full-frame and nothing for either of them with any extenders (1.4x or 2x).
I'll just have to hope that someone is good enough to add them to the lensfun database.