Gidday Jamie
If there is an adjustment at the accelerator pedal end, back it right off. Ditto the throttle idle nut on the carby body.
These things may just allow you to get sufficient cable length to allow you to clamp the cable on at the carby cable connection.
If that doesn't (or can't) work, you can shorten the outer cable sheath, which effectively lengthens the inner. Might make the throttle a bit jerky, but it will get you working again. You might have to do this at the pedal end to preserve some semblance of alignment at the carby end ...
You may need to cut the frayed cable end off to allow it to feed back through the hole in the clamping nut.
Hope this helps.
Sorry I can't be of more help.
I have never even seen a Justy ... :iconwink: