I am basically agnostic whether to order the middle movements, Scherzo first followed by Andante, or reversed. I believe a persuasive interpretation of the entire symphony can be achieved, either way.
When I first encountered Mahler's 6th was during my junior year at Occidental College. I had not yet heard anything like the 6th, not even any other Mahler Symphony, including the 1st, 2d, 3rd, 4th, 7th, 8th, and 9th Symphonies. The 6th shocked me with its militancy mixed with fury in the 1st Movement. I had to play the 1st Mvt. over several times before I could proceed to the 2d, 3rd and 4th Mvts. I have always loved marches, since I was a little kid. Once about age 6 or 7, my sister gifted me with passes to see The Captain from Castile. I so loved the march tune and accompanying scene in the film, my sister gave me the soundtrack recording for Christmas. She told me many years later that when the march music commenced I would stand up and begin waving my hands in strong chopping motions, while my face turned red, veins in my temples bulged, until I was perspiring copiously and out of breath. A few minutes later I wanted to do it again. I was told by our mother I would have to wait until another time when there were fewer people (like, none) around.
So, the vigorous march rhythms and flourishes in the 1st Mvt captivated me, and I started conducting all over again, physically or in imagination. I believe clearly defined, step-wise progress through each of the four movements is key to interpreting the music. The 1st Mvt Allegro Energico tempo should be a brisk but not hurried march step, about crotchet equals 120bpm. As it happens that is closest to the tempo Jascha Horenstein takes in the 1st Mvt, though several other conductors are in that general tempo range, 120-132 or so. The important thing is each step must register decisively and deliberately, like a well trained company of soldiers would be taught to march, left-right left-right etc. There can almost be discerned a "get out of my way, I'm coming through" resolve and decisiveness in each step, whether it is hear aloud or just "felt" as the sections play out. The basic tempo can be modified, for example, at the entry of the Alma second subject, broadened a bit for a couple of measures, but must then be a tempo, passing up the temptation to broaden again at each iteration of the four upward notes sweep, or variants of it. I like Maazel's tempo mod for Alma in his recording with the Concertgebouw Orchestra, but feel it gets a bit carried away with itself, so there's a feeling almost of listening in slow-mo; and it can be queasy making some times. But, as I said, I like it. It is in the spirit of the overall tempo scheme, which is always some form or play on the march rhythm. Even in the quieter passages, still a subtle tick-tock should be felt if not heard. The cumulative energy, feeling and power of the march rises to astonishing heights at the conclusion of the movement.
For the 2d Mvt I prefer the Andante to come first. I never have felt entirely comfortable with Scherzo followed by Andante followed by the Finale. Barbirolli's studio recording with the New Philharmonia was my reference, but even his ordering (or what I thought was his choice of order) didn't persuade me that it was the right one. Until only recently, it hadn't occurred to me that possibly the order EMI imposed wasn't Sir John's choice. Now I believe I understand what felt wrong to me. The key factor again is tempo and the rhythm of a march, or, in the Andante, a step as though on a leisurely walk through the garden or the forest (die Wald), observing both past and present delights and treasured moments. The movement should be calm and fairly cool, even when things get louder and more hectic, there should be a sense of the need to return to the initial walking tempo which evens matters out. I don't believe the Andante is a large scale tragic outcry or lament, it just isn't in the notes here, which are simple to the point of naive, a child-like consciousness in the midst of bigger things developing in the other movements.
The Scherzo should be sharply accented and weighted on the heavy side. It's a bit of a peasant dance step which beat is elaborated on and transformed. It's a bit spooky, too, as only Mahler could be spooky and peek-a-boo. But there is always deliberate progress through each development so as not to bog down or become frantic, just moving on and along.
The Finale, once again, there is the extraordinary march rhythm which plows through every obstacle, scales any and every height, and retains its footing throughout. The interlude section, mysterious sounding as it is, must also give way to the march tread, which has an unmistakeable feeling of inexorability.
Tempo, then, I believe, is the key to each and all of the 4 movements of the Sixth. Other considerations are welcome, but any scheme must come to terms with the stepping/marching rhythms.
Enough for this writing session...