Gummy worm plug ought to be way more than enough for that little thing. As for being near the center of the tire, that makes no difference. The plug will work anywhere in the tread including all the way out to the edges where the tread meets the side wall. Gummy worms usually are not slung out of tires. Rather the wet cement lets them squirm into the tire. This usually happens because the worm was cut off flush with the tire. Cut the worn off about an 1/8th inch above the tread. Thus, some of the worm is left to mushroom over and prevent squirm from allowing the worm to retract into the tire. Some people put the worms in dry, smaller punctures for this reason. I use cement as a lube for intallation and as an adhesive seal when it cures. A worm installed this way can be ridden on right away without having to wait for the cement to cure.
Aside: There is a long standing argument that plugs in a sidewall are an absolute NEVER. I have plugged sidewalls to retrieve myself from remote and considerably more hazzardous problems. Once the initial crisis is over, I won't ride on such a plugged tire. One does what one has to at times.
"beware the grease mud. for therein lies the skid demon."-memory from an old Honda safety pamphlet