Hello,
I hope by now you have made some progress in your gas assist, but if not, might I offer my 2 cents worth of opinion:
Initially, when first reviewing the part, I must ask "why gas it at all - why not add ribs since it seems you have 4 side/slide actions to begin with and could probably add an equivalent number of ribs for the strength requirements.
That said, if you still must gas, the only advice I can offer is:
I would start with full shot and over flows, the displaced volume of the desired channels most likely will not fill the remaining 25% or so of a short shot as you have set up in one of the images. You should be able to calculate a best case volume of the desired gas channels and fill accordingly, but a center of mass polymer gate will probably prevent any effective short shot use.
Then try to modify the geometry to include a molded in manifold for a single gas input location to create a channel to all 3 ribs.
Let us know what worked.
Good Luck - SPS