I have been playing with jump distances and the HabHyg50ly file Winchell Chung has provided on his Project Rho site. If I set the maximum jump distance to 3.5 parsecs then all but one star in the list is reachable from Sol -- a K0 solitary that is on the edge of the map. Since that is near the edge it would probably be reachable if we had more data.
That leaves two tricks. The easy one is to establish costs and approximate travel times, trying to make sure that a 50ly sphere is plenty. A hard one is finding a way to justify the 3.5 parsec maximum, and the costing structure.