I always resize first, then trim. I also use a Lee trimmer and don't seem to have any problem getting the pilot into the neck.
Two things pop into my head:
1. Maybe the neck sizing plug is undersize.
Or;
2. Maybe there is a lot of powder residue in the necks of your fired cases.
Try cleaning out the necks with an appropriate sized bronze or nylon bore brush. If that doesn't help, try borrowing another sizing die. If that fixes the problem, call Lee and tell them about the problem. They will probably send you another plug for your die, if not, a new sizing die.
Hope this helps.