The cache is not at the posted coordinates. Solve the puzzle below to find the final location.
Penguin Peter is not a numerical sort. He only deals with letters and words. Looking at the coordinate words, he realized that if you spelled out those coordinates, it would take anywhere from 16 to 23 words. For instance, the least word count could be for example:
north zero degrees thirty point five two nine west ninety degrees fifty point zero one seven
while the longest might be
south forty six degrees twenty six point seven five one east one hundred and sixty nine degrees forty eight point two zero seven
After his last encoding, he realized he was maybe being too cryptic, and the final encoding was just too long, longer than his friend Paul's. Being a clever sort, Peter realized that you didn't really need all those letters, you could shorten it based upon the words "in context". For instance, the first word can only be "north" or "south". Then, say, if the first two words were "south twenty", the third word could only be "degrees", or "one", "two" ... "nine", only ten possible words. So he set about creating a short encoding for each of the 16 to 23 words. The encoding was this:
For each possible word in context, sort each of those possible words alphabetically. Assign a letter from 'A' to 'Z' for each of those words. Some contexts have only one possible word; the most in one context is 28. Since Peter doesn't like numbers, he chose Greek letters for those counts above 26: 'α' (27), 'β' (28) (though he didn't need them for this encoding).
In the end he finished off with this result.
You can validate your puzzle solution with certitude.
Congratulations to KendraH for FTF, and jeremiahsjohnson for FTS!
Update 12/7/2018: Otters are smarter than penguins, or at least more careful. An obvious digit has been fixed. Also for the purposes of the calculations above assume that there’s neither North or South ninety degrees, nor any East or West one hundred and eighty degrees. There is however, both North and South zero degrees zero point zero zero zero minutes, and similar duplication along the meridian. Further clarification: for the purposes of this puzzle, assume all penguins are confused and would use the word "degrees" even for the number one, i.e. "one degrees fifteen point ..." instead of "one degree fifteen ..."