I think your instincts are correct. Wider pipe will certainly help. I think you'll still be in turbulent flow (I'd estimate somewhere around a Reynolds # of 3000) but it will be nearer the transition to laminar (Re ~2000) and should make the pressure drop significantly less.
In the vernacular, as you approach laminar couette flow (with wider pipe), the flow at the pipe wall is able to be apporximately zero (no-slip boundary condition) instead of skidding along, bouncing into the 'roughness' of the nylon, and causing turbulence in the flow. The wider the pipe, the better.
Of course, the last time I worked a problem similar to this, it was for plasma flow confined in a magnetic field (the 'pipe'). Same equations, though... I think.