Are you also enabling God Mode? Keep in mind, God Mode doesn't always enable, you have to watch on the left side to see if it says Enabled or Disabled and may take 3-4 tries to enable.
I just tried with no trainer and built prefabs until I ran out of materials. Then I enabled the options and was able to continue on as much as I wanted. The trainer worked ok for me.
Haven't played Nuka yet but from all that I've read, I don't think getting more Cores that aren't from the quest will advance the quest. ID# is said to be 0601E367 to get more in the console but the problem is they won't advance the quest stages.
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