It would take a major increase in raw stuff for Stroman to just double his strikeout rate and considering his body size I can't see that happening. Kershaw introduced one of the best pitchers in his slider which helped the K rate surge and Kluber always had a whiff rate over 10%, I don't see how they compare to Stroman.
I think Stroman can get his K/9 in the 7 range maybe even approach 8 but it seems unrealistic to expect it to jump up over 9.