Simply having water present over the septic sewer is not going to result in any substantial mixing at all. I asked, but didn't get an answer to what the significant mechanism of sewage dispersion was. I thought about it and here it is:
Sinks, showers and toilets are all connected together in NO I assume, because they probably don't divert grey water. Grey water is effluent from such things as sinks and showers. The drains for the sinks and showers are all higher than the manhole covers/vents by several feet and as long as the surface of the flood water remains below any particular drain, water will flow down the drain and push sewer water out some hole/vent/seems somewhere in the city.
As long as the toilets aren't used and water use is minimized I don't see a serious problem in the short run. Flood and rainwater flows, or presence do not cause significant mixing, or flows. P traps under the sinks can even be disconnected and 5 gal buckets used to collect water to be dumped in an outside pit later.
The toilets will be used but what is the big deal? There are sewage spills all the time. Big ones. It is not a big deal. The whole area is going to have to be cleaned anyway. It is not creating any further damage.