You're right, to me it was a mix of a looped march which was asynchronous to any band shown and, as you say, a constant level. Big Ben's bong and the guns in Hyde Park were added in as their level didn't change even though the camera position in relation to them did so.
However, both of us shed a few tears with the removal of the monarch's instruments as if to say "your job is done" swiftly followed by the lowered coffin and fading piper's lament. RIP.