I have just made one for the Badger using 8mm Marlow Excel Fusion. This has dyneema in the inner, and also in the outer and so is excellent for tapering. It is rather expensive though.
Essentially for tapering you just need a rope which has separate inner and outer. Then, you cut the outer off, and tuck the end back inside the inner so it ends up tapering nicely between the rope diameters.
If you get some rope I don't mind doing it for you up in Scotland at the expense of a beer
I am going to be there from Saturday, so the sooner you can get me the rope the better. Also, if you have the old rope to get the taper in the correct place that makes things easier too.