March in Canon to begin my symphony

So I had this idea to have a march in canon. So I would have a rhythmic cell like this:

to give a march-like feeling. I have decided on 6 rhythmic cells before a note change and going up 1 note and then down the entire major scale. To make this not seem boring, I decided on having the march in canon with 3 lines(second line comes in 3 cells after the first line, third line comes in 3 cells after the second line). I also decided to have a close transposition, to make it sound like there are chords being played. So I tried starting with a 3rd transposition and just 2 lines. But this lead to there being a second between 2 notes which was repeated. I figured this was too dissonant, even though I usually think of the most dissonant interval as being a tritone. So then I tried a 4th transposition and it sounded beautiful, with only 2 dissonant intervals, both being tritones.

Adding a transposition by a third on top of that meant many more tritones, diminished chords, incomplete 7th chords, sus chords, and probably some chords that you could only describe by the details of the intervals. But I was wanting it to sound like chords, just not with a lot of dissonance. I got second inversion C minor chords this way and of course, the ending tonic major chord. But those are about the only consonant chords I got.

But would a transposition by a 5th for the second line and a transposition by a 4th from the second line for the third line, which would ensure consonance be considered close? I don't think so because then you have basically power chords throughout. Transposition by a fourth over another transposition by a fourth would give a lot more sus chords in second inversion, a jazzy chord. Not what I was aiming for either. So if this won't work, will I have to adjust transposition chord by chord to make it sound like major and minor chords(which is what I was aiming for, not dissonance or a jazzy sound).

This march in canon idea is really an idea for a theme in a symphony related to war. I figured that if I could put a symphony to words, it would be easier to write and not so overwhelming.

So how can I have a close transposition in all the lines while also ensuring consonance with maybe a few 7th chords or diminished chords where I get those tritones in the first 2 lines? My canon I plan on being a strict canon, so timing and pitch are the only ways to tell the lines apart.