The following is the best I've been able to come up with so far, as a practically feasible experimental demonstration of the backwards sound phenomenon:
A plane traveling forwards at Mach 2 fires three exploding shells backwards, at speeds of Mach 1.2 relative to the plane, at times t, t+1, t+3, each programmed to explode after time T, which is the minimum time such that the explosion would be far enough away from the plane to not endanger it.
The shells explode behind the rear boom, at times t+T, t+T+1, t+T+3, and in each case is at the same displacement vector from the plane at the time of the explosion. So we can consider those explosions as part of the supersonically moving phenomenon or system of the plane.
The intervals between explosions, in the reference frame of the plane, are 1 second, then 2 seconds.
But for an observer on the ground that is well in front of the location of the last explosion, the explosions are heard at intervals 2 seconds, then 1 second. That is, they are heard in reverse order.
Because the shells were traveling subsonically prior to exploding (at Mach 2 - 1.2 = 0.8), there is no sonic boom of the shells to complicate the analysis.
In the above scenario, the backwards pattern of shells is heard after the boom.
If the shells were instead fired forwards, a ground observer in front of the plane would hear the explosions in reverse order before the boom, but the analysis would be complicated by having to consider what effect the sonic boom of the shells themselves (which are traveling at Mach 3.2) had on the sound wave of their explosions.