That is pretty much my plan. I just got to thinking, it is about 10° from the plug I put in a screw hole. I am going to go look and measure and see if it posible that the screw cut the tire bead. If it did the Avon gets crap canned.
How long was the screw? I doubt it. Unless you plugged a side wall. ??? Even if the screw dropped inside it's highly unlikely to do any damage at the bead. And that bead is one tough hombre.
Repeated tire changes begin to build a fair amount of crud on the rim preventing a good seal. Shops should wipe down rim lips with a ScotchBrite pad before new mounts. Most do not. I've had a couple rim leaks, but only before I started changing out my own tires.
I don't believe any type of tire sealer will remedy a bead leak, maybe.
Tire should be broken down as mentioned and both the tire bead and rim lip should be scrubbed with 3M pad. Heck, might just be a good time to replace the plugged tire too.