I take it you can move the rotor around on the hub, it just won't pull over the parking brake shoes, correct?
If this is so a ridge of rust has developed on inside of the drum and will not let the shoes pass. Now you must get over this ridge. You will need to adjust the shoes down to do this as I think you have concluded.
A screw driver will work just fine to do this. Look into the hole with a flash light, as you turn the star wheel you should be able to tell if your going in the right direction. If not turn it the other way. Mark on the rotor the direction you need to turn it, as this comes in handy when you adjust the shoes back out. You will have to push the star wheel hard as there is usually a spring clip that is there to resist movement.
You may find that even with the shoes adjusted all the way down that you need to work the rotor off.
Once off check the park brake shoes for damage or loose shoe material. Many times rust will develop on the shoe web between the bonding of the material and cause it to de-bond. and this will cause the problem you are having.
If the shoes are bad replace them. Make sure the axle hub surface is clean and free of rust. Install the new rotor with a thin coating of silicon grease on the hub surface, Install a couple of lug nut to keep the rotor tight against the hub and adjust the star wheel back up until the shoes make contact with the drum and you can feel a drag. Hit the park brake pedal a few times this will ensure the shoes are centered. Adjust more if needed. Now back off the shoes just to the point that you feel no drag.
This should do it and you most likely will not need to mess with the cable adjustment at all.
Mike