Can you get a septic pumper truck to the area? Or, at least close enough to run their hoses?

I'm not very familiar with the siphon systems and it sounds like the inlet is just buried. This probably means the inlet pipe also has muck built up in it.

Use the pumper truck to get all the mud from around the inlet and as much from the inside as possible. Then use a trash pump and smaller hose as a water jet to flush the inlet pipe out.

Does the system have plumbing that extends above the dam soils that can be used as a cleanout port?

Fish on!,
Noel