I'm sure a reason for all this marching is the obvious one that Mahler grew up within earshot of a barracks, and all the consequent march music he'd had heard from the start.
Interesting, too, that someone isn't too keen on M6 cos "there's too much marching."
Insofar as existentialism is tied to questions of existence and the here-and-now (where existence just is), I'd take mahler to be very existential, partly because hasn't he spoken about much of his music in terms of existence, and partly because he was a Cancerian.)
I say the last a) despite having a philosophy degree, b) cos I'm Cancerian.
Speaking from the inside, cancerians are moody, touchy, sensitive etc. exactly because they are (naturally' (?) attuned to moment-to-moment reality, consciously or unconsciously. Partly. And they are quite likely to respond, even react, to everything they experience, often immediately. Thus, some of M.'s tantrums, etc.
(Hence also Mahler's openness to 'the mood of the moment' in performance, and to performers after his time responding to the acoustics they find themselves in.)
Another counterposing to existentialism (apart from essence), is knowledge. Whereas in Anglo-Saxon philosophy a theory of knowledge is a basic starting-point, Continental philosophy is often more interested in the nature of existence.
Incidentally, Alma was a Virgo (born 31.8.1879). She had a Leonine mode of expression.