Plug it and run it to the end of it's life. The sticky string plugs are self vulcanizing. If you don't know what that means, look it up in the dictionary. Not a slam, just a better description than I'm willing to type here.
I've run plugged tires to the end of their lives, 4k on one tire, about 2500 on another. Never leaked any air. Do NOT use the BMW/Stop-n-Go muchroom plugs and expect them to last the life of the tire. They can be excellent for road side repairs, but the end will wear off or the plug will break and the result will be rapid deflation. Not what you need. If you use one of those on the road, do a better patch job after you get home.
The inside mushroom patch is glued on from the inside with a part of the patch inserted into the hole. These are excellent and last for the life of the tire. Probably the best method if you're willing to dismount the tire from the wheel.
The State moto cops around here get a lot of flats due to riding on the shoulders so much. Their policy is to plug a tire twice, and only a second time if it's in a different quarter of rotation on the tire. No sidewall repairs. A third puncture? Toss the tire. Not a bad standard to follow. After all, they ride at speed, so they're not going to take chances.