I'm currently going over lesson no. 21 of 新完全マスター N2, and I'm not sure about the difference between the usage of ~まで and ~さえ. Looking at the description and the example sentences, it seemed like both of these forms might be used to mean "even X" or "to the point of X". The example sentences that really bugged me are the folowing:
仕事がとても忙しいときは、会社に泊まることさえある。
遊園地では、みんな長い時間並んでまでジェットコースターに乗りたがる。
In which both さえ and まで are used as "to the point of", and
一番に賛成してくれると思っていた母まで私の結婚に反対した。
この料理は簡単だ。料理の苦手なわたしでさえ失敗しなかった。
In which both さえ and まで are used as "even" when presenting an unexpected/atypical example.
In addition, according to Shin Kanzen, the words coming before these two forms are both "極端で意外性のある例".
I'd be glad to know whether both of these forms can be used in the same way in these contexts, and are they interchangeable in the sentences I mentioned earlier? If not - when will each one of them be used?