I agree. The new disks will compress against each of the waffle washers (buckle washers) and will tighten enough to get the castle nuts on.
I put a new set on a few years ago and had a similar problem, but when I evenly tightened the nuts, I was able to get the cotter pins in.
Do not use lock washers. You must use the castellated nuts and cotter pins. The disks will wear over time and so the lockwashers will not do the job. In fact, you should check the disks often after installing new ones, as you may have to tighten them once later.
I put a new set on a few years ago and had a similar problem, but when I evenly tightened the nuts, I was able to get the cotter pins in.
Do not use lock washers. You must use the castellated nuts and cotter pins. The disks will wear over time and so the lockwashers will not do the job. In fact, you should check the disks often after installing new ones, as you may have to tighten them once later.