When you buy a retrofit kit for heated grips to a K11LT, a new handlebar is included.
Looks like a PO have been a cheapo and tried to save some money.
The bars for heated grips have a cut out at the end for the wiring.
(see attached picture).
Should be possible to make these cut outs with a angle grinder, just be shure that you
round all sharp edges.....especially on the throttle side.
£ 130,- is for new grips only, you probably need a need a new intermediate wire also
since the resistance wire allready is fried (worst chase scenario....a fire on the
underside of the tank, while driving.....the chance is minimal but,but,but).
At least have good and long test (~0,5 hour?) with the grips on the low position
before putting the tank back on (and keep in mind that the wire would get a bit
hotter when the engine reaching operating temp and stays there for hours and
the area being more closed when the tank is back on.
It's your call, good luck.