If it was me - and I am glad it is not - I would go with a larger and larger bolt extractor. At some point I would expect that it would work.
We're talking EZ outs, right? They look like this:
This is a follow up note just in case others find themselves in a similar situation with this oh-so-popular outboard. I tried an EZ Out once more, this time with the motor oriented in a way to really see the tool at work. I quickly came to the realization the tool applied so much outward force on the plastic plug that turning it loose would be impossible.
Instead, I keyed a notch into the plastic using the tip of a boning knife. With the knife's blade firmly inserted into the notch, I was able to unscrew the plastic plug's remaining part. The whole process took less than 2 minutes and left the oil pan's threading intact.