Conor,
I would try to pull a drawstring through first - hit, and overcome, all the snags and route smoothly without possible damage to the 6mm cable.
I think you would benefit from a hole at the wall where the cable goes the wall to the charger to make feeding the cable as easy as possible.
I have used a piece of wire taken from a stock fence to do similar routing instead of the fibreglass rods. You can bend it when necessary to go over or under awkward points.
Also, when you start pulling the cable with the drawstring, have someone feeding the cable in the first hole to reduce tension in the string and the cable. This also minimises damage to the outer insulation.
Good gaffer or duct tape is very useful for this job.
Best of luck with this.