This all sounds like myth-type stuff to me. I took the JFK-HKG and HKG-JFK flight several times during it's short life.
1) Each time the Westbound flight to Hong Kong went up over Michigan/Minnesota, then southern Canada + Anchorage.
2) The return Hong Kong to NY did a similar path, actually flying over Chicago, slightly south of the west bound flight over eastern North America.
So, if the polar route and radiation is an issue, then NY versus Chicago is a non-issue.
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- Bob