[FiatLuxDave]

Just to point out a design assumption here, saying that an exponential amount of fuel is required is making 'the rocket assumption': that both the mass and energy required for momentum change are carried with the vehicle, and are expended upon reaction mass.

For travel between star systems, these assumptions do not need to be true. For deceleration, it makes more sense to transfer the original kinetic energy out of the vehicle's movement than to expend even more energy on accelerating reaction mass yet even faster in the original direction of travel. Remember that you have a whole star system of reaction mass at your destination. There may be engineering challenges, but there is no physics reason why you couldn't expend your original energy in "pushing off the sun", and then recover it by "pushing against the new sun" when you arrive. Depending upon efficiency, this could then leave you with the energy for another flight (perhaps home).