As the authority have admitted issues with their website and are willing to accept an emailed challenge, take advantage of it...copy your email and their reply with any challenge.
As PMB says, loading is an exemption and while this would normally be judged against need, ie to carry a heavy or bulky parcel, claiming it should do no harm, they should re-issue the discount and if they fail to, given the emails, that would be an argument to take forward which could win the case on its own.
Include a copy of any post office receipt and if the parcel was large or heavy, detail that...