You'll collect much more ionizing radiation on the way there
That depends on whose figures you use.
On one set of numbers, a five or six hour turnaround is going to be equal to two month's of local flying.
So no, you won't collect more on the way there, but it's not a show stopper.
5 hours in NRT = 0.33 mSv (current worst case), therefore 18 trips is the same as your entire year's worth of flying.