There are a couple options to saving fish...none are inexpensive.

One is to dig a holding pond and the second is to build a coffer dam inside your current pond basin after lowering the water level. The coffer can also become structure, plus deepening the current shallower end for an area for future sediment to settle in.

Personally, I'd opt for starting over, as it will be the overall least expensive.

Get permission from your neighbor below to let water flow and give him most of your "major fish". Breach the dam, and doze the silt out of the breech, haul the spoils off or landscape an area. Repair the breech and let it refill, then restock as wanted.