Generaly speaking, downmixing from a multispeaker configuration to stereo is a tough task. Is not at all straightforward. Its not technical but aesthetic. It provides a shift of the presentation of the sound material, a transcription from surround / imersive / omnipresent (multispeaker) to confrontatial (stereo). This shift is very critical to the perception of the sound meterial. Whether it works or not is dependent on the compositonal role of space articulation. In other words, if space and spatial movement is inherent in the composition approach.
Anyway, downmixing is a compromise and it should be regarded that eventually distorts or collapses the spatial image. In some cases, where spatiality is a structural element of the composition, it is impossible to downmix without destroying the piece.
Going to your case, here are some points:
One solution is to transfer the 8-channel mix to binaural (as billyhologram suggested). This approach, shifts the composition space from the “room space” to the “head space”. From one hand it retains all the spatial dimensions / trajectories. On the other hand restricts listening experience to headphones. Furthermore, by listening the binaural mixdown from a stereo system, an overall sense of the compositional space is retained but the whole spatial image is somehow “blured and compressed”.
A 2nd fast but crude approach would be: If a) the sound space is considered as a circle around the listener, b) sounds are placed only in the perimeter of the circle and c) rotating trajectories is the only spatial movement, another solution is to downmix by interleaving the channels.
From this image
_1-2
8----3
7----4
_6-5
Go to:
hard left: 1,3,5,7
hard right: 2,4,6,8
This solution keeps all the rotation movement in stereo speaker reproduction but the sensation of the rotation speed is increased.
A 3rd solution is to place the 8-channels in stereo as if you are listening to the 8-speaker configuration outside the circle. Narrow the image of the two front/back channels and place them towards the stereo center, keep the side-front pair to the stereo extreme and the side-back pair slightly narrower. Also drop the level and delay by a few msecs the back channels (as already suggested by eesn).
From this image:
_1-2
8----3
7----4
_6-5
Go to this:
left - right
<--------------->
8 7 1 6 5 2 4 3
This solution works best with spacial images placed “within” the circle rather than in the “periphery”. It should work mostly with static sounds but on the other hand it should distort the rotating trajectories of moving sounds
