My opionion: Plug it with a sticky string and ride on it. The tire will not push the rope out (ever try to push a string?) There is no catastrophic failure mode here. The worst possible scenario is that the rope would let a little air seep- in other words, you'd be back where you are now.
I've ridden many miles with rope plugged tires, and I can watch their 'health' with my tire pressure monitors. They haven't leaked at all- not a bit. This has given me a lot of confidence in these repairs. When you finally take the tire off you'll find the string has permanently bonded in a mound to the inside of the tire.
I can't say the same for plugs, although lots of people like them. I have seen those fail several times.