I got a roofing nail in my Continentals after only a couple hundred miles after replacing my K3 due to a nail. The K3 had 1800 miles so I didn't mind replacing it, but a couple hundred? I plugged it with something like this:
Slime Deluxe Pistol Grip Tire Plug Kit | Tire Repair + Sealant | Northern Tool + Equipment
Sticky, black things, not a patch. I was told to not go fast on it, yeah, ok, of course. But how could I not?

It held for 4000 miles until the tire was ready to be replaced from tread wear. That was doing at least 80 mph daily for 30 minutes.