hi have had same probs in past and had a go a few different ways.
this is how I go about clearing the carbon.
pour neat petrol into exhaust and leave to soak for 2 or 3 days.
pour petrol from exhaust into container.
making sure all the fluid is removed i take a blow torch and heat up from the end that joins to front pipe untill i can see the carbon glowing red. then i prop exhaust up near vertical and place my fan heater so it blows air into and up exhaust. will fan the carbon and continue to burn for 2 or 3 hours. once cool i steadily bang it on chock of wood with a bit of old carpet on it to save any damage. loads of burnt carbon dust comes out. then i take bike for a good long blift to clear any leftovers.
hope this helps you out mate it works for me!