In this work, we modify the standard flux tube simulation domain to include arbitrary ion gyroradius-scale variation in the radial profile of the safety factor. To determine how to appropriately include such a modification, we add a strong ion gyroradius-scale source (inspired by electron cyclotron current drive) to the Fokker-Planck equation, then perform a multi-scale analysis that distinguishes the fast electrons driven by the source from the slow bulk thermal electrons. This allows us to systematically derive the needed changes to the gyrokinetic model. We find new terms that adjust the ion and electron parallel streaming to be along the modified field lines. These terms have been successfully implemented in a gyrokinetic code (while retaining the typical Fourier representation), which enables flux tube studies of non-monotonic safety factor profiles and the associated profile shearing. As an illustrative example, we investigate tokamaks with positive versus negative triangularity plasma shaping and find that the importance of profile shearing is not significantly affected by the change in shape.