While you are testing things at the range try a pressure pad at the end of the forestock.
All my older Remingtons had this feature, I don't know if Remington still does this or not.
However I have a Savage and Stevens, they don't have that feature and they don't vertical string.
Another thing that can cause vertical stringing is erratic ignition. If you are using handloads you might want to check your primer seating.