Poached eggs at altitude?
I live up in the mountains. Two things I do not do are: a) remove food from heat and expect it to still cook properly, because boiling points are lower at higher altitudes; and b) use the cited time in the recipe. I always add time, because the lower boiling point means more cooking time is necessary. Also, try not to open the lid of the pot unless you absolutely have to. The lid provides some added internal pressure for the pot, which helps with cooking, and keeping the lid on as much as possible provides steady heat. Other than that, I have no suggestions.