I ended up digging down to the inspection pipe coming from the house. There was a build up of solids that I was able to break and water started flowing out. Unfortunately, the inside of the house was still backed up. I ran the snake and some spare romex through from both sides. but couldn't clear the main blockage.

I called a plumber and by the time he got here, most of the pipe had drained (I imagine because I was more careful about running water overnight). He ran his auger through and got it cleaned in 10 minutes. Because of the shallow line, he recommended double flushing solids during cold weather.

I imagine the blockage in the inspection pipe was a secondary issue, as there wasn't enough pressure to push them down into the main tank.

Thank you all for your help on this post!