Based on a previous question, you have a smoky flame, a gosh-awful mess in the firebox and the nozzle drips when not running. There is currently no fuel oil cutoff solenoid, as you said that the pump output goes directly to the nozzle. The pump produces 100 psi when running, which you say is within spec.
Replacing the pump may improve the situation. The dripping at the nozzle is probably due to the pump being worn and allowing fuel oil to seep through the space between the gear pump's "teeth" and the walls of the pump chamber. Since the fuel oil level in the tank is higher than the nozzle, there's a small head pressure and over time a significant amount of oil can get through.
It would be much less expensive than pump replacement to add an aftermarket electric solenoid fuel oil valve as a positive cutoff when the pump and blower are not running. This seems a reasonable alternative, since the pump is producing adequate pressure. If this is available, the only fuel that can dribble out after a flame cycle is a drop or two due to expansion as cold fuel oil in the nozzle assembly heats up by being in a hot firebox after the flame goes out.
If you have air in the fuel, you can actually get a little stream of oil after the flame goes out due to the air bubbles expanding as the pressure drops.
Air bubbles in the fuel oil can also cause an unstable, smoky flame. Air can be introduced by a loose or poorly made-up flare fitting in the fuel line on the suction side, an imperfect seal on the fuel filter housing, etc.
Can a worn pump introduce air? What if the shaft seal on the gear pump is worn? Could that pull air through the seal on the suction side and be the cause of all of the problems? It's possible, but I can't say how likely this scenario is.
If you could hook up clear tubing to the pump output and run the fuel oil into a container, you'd be able to see any bubbles. There shouldn't be any. If you do get bubbles and all connections are tight, you need a new pump. If you get no bubbles, I think your best approach is to add the electric valve.