Firstly "latest" does not only mean "most recent". The word "latest" can be used in discussing events at any time, including the future, and is part of canned phrases such as "at the latest". We can say that "the latest you should pay that bill is the 31st of this month", but not "the most recent you should pay that bill is the 31st of this month". The word "recent" takes a relative point of view from some time understood to be current; the most recent event is the latest one, excluding ones that have not yet happened.
"Most late" does in fact mean "latest". Both express the superlative of "late".
Though awkward, it is possible to say "the most late you should pay that bill is the 31st of this month". It's only awkward because "most late" is a verbose phrase that isn't used much, since the direct superlative "latest" is available. The "most " construction is required for adjectives that don't form superlatives, or do so awkwardly.
An example of a class of adjectives that don't form superlatives are those which are verb participles, or have that form:
Out of all the cynics I know, Bob is the {most jaded | *jadest | *jadedest}.
We have no choice but to use "most jaded".
If several people have arrived late, we can say "out of the latecomers, Bob was the most late" or "out of the latecomers, Bob was the latest".
Now if you say "the November 11 interview is the latest one I saw in the schedule", there is an ambiguity there. Does "latest" refer to the date of the interview? Or does "latest" refer to your discovery: is it the most recent one you learned about so far? The ambiguity is resolved by the context given by the prior discussion and by other knowledge of the world, such as that a person usually has the entire schedule before their eyes; people usually don't report about the incremental discovery of the elements of a schedule. However, we can avoid the ambiguity anyway, like this: "the November 11 interview is the latest dated one I saw in the schedule".