Excepting the obvious case of a cold pipe, or indoor temperatures not much warmer than outdoor, smoke roll-out is nearly always a function of fireplace (or stove door) opening size to flue cross-section. Simply put, it takes a bigger pipe to prevent smoke roll-out on a bigger opening. So, if that stove has double doors, you might do well to work as much as possible with just opening one of the two doors.
For an absurd case in point, look up the chimney of any cooking fireplace, such as the one shown in my avatar. With fireplace openings of 20 - 40 square feet, you'll see a flue large enough to understand the origins of any story of people or jolly fat elves entering a house thru the chimney. Santa didn't have to squeeze down to 6" diameter, in the 18th century.
But he still had to contend with the fire at the bottom!