How much slope are we talking about here?
Sounds as if it wasn't built correctly; ideally, you want your septic lines to all be equally full, i.e. dead level. It is possible that what was done, but your clay soil is forcing the water out at the low points on your slope. My drain lines are set into a steep,slope, but they do cascade top line to bottom line in the clay soil, and we have no issues. This leads me to suspect that your water table could be generally high in your low spot, leading to issues.
What do you mean by "emergency area"?
I would be inclined to do as your septic guy suggests and build up the lower ground with sand gradually until the soil is dry and stays dry. There are some nice YouTube videos on how to do it, but you keep spreading 1/4-1/2"of sand into your grass (you can use a Scott's lawn spreader), then let the grass grow, then spread more in. You use a rake and extra sand to manually fill in any excessively low spots. Basically, put the sand in as fast as the grass grows, although by the sound of your second post, you may want to go whole hog and add a foot, or three, of sand topped by enough topsoil to get a lawn back.
I am assuming that your septic tank has been pumped and that you don't have a water leak in the house.
All the best,
Peter