The dirty secret of the symbol "ə" is that when used in transcriptions of English, it doesn't actually pinpoint a particularly specific vowel sound.
Rather than being used as a strictly phonetic transcription, the use of the symbol "ə" is usually based instead on simplified, standardized conventions. Normally, that does not pose a problem because these conventions are sufficient to indicate the contrasts that differentiate words by meaning in English (phonemic contrasts). But when you're dealing with something like analyzing the quality of a vowel in a song, conventional IPA as found in dictionaries won't serve you very well—dictionary-style transcriptions aren't suited to showing the phonetic details of all the slightly different ways that a word can be pronounced.
One conventional use of the letter "ə" is to transcribe a fully unstressed vowel that is usually short in duration, unrounded, and has a quality that is usually somewhat intermediate or unspecific (we can say that it functions in the sound system of English as a 'reduced' vowel). The unstressed vowels transcribed with "ə" are not all exactly the same; rather, this transcription covers a range of similar qualities, some of which are more or less common depending on the context (e.g. if they come at the end of a word, before /t/, before /p/, before another consonant...). Some phoneticians prefer to reserve "ə" only for unstressed reduced vowels of this type (in the context of phonemic transcriptions of English).
Other transcribers adopt a convention of also using "ə" to transcribe the stressed vowel found in words like strut and nut. There are some practical and also some theoretical arguments for this practice. For the sake of this answer, though, I want to emphasize that although this stressed, unreduced vowel often has a quality that is similar to an unstressed reduced ə vowel, it is not necessarily exactly identical to it.
For many speakers, the unstressed reduced ə vowel is not always clearly distinguished from an unstressed ɪ vowel. This is called the 'weak vowel merger'. I have this merger, and it sounds like you have it too. I expect this is why the audio files from OED and Merriam Webster sound like /ˈkrɪsmɪs/ to you. It doesn't sound exactly like the vowel in 'must' because when stressed (as it is when pronounced in isolation), the word must has an unreduced vowel and so its vowel does not become merged with ɪ.
In the context of Mariah Carey's "All I Want for Christmas Is You", I think what's happening is that the vowel has a different quality than you would normally use in an unstressed syllable because she extends the vowel sound quite a bit relative to normal speech.
Here is a paper on the phonetic quality of schwa vowels that I found helpful: "The phonetics of schwa vowels" by Edward Flemming. (I found it when working on an answer to this previous question: Why is the pronunciation of "Exodus" different from the spelling?)
