Small pond filling in

I have a small duck pond. 3 feetish deep. 13-30 rectanglish. So last year our two pigs gleyed the pond wonderfully. Now the problem is that our 9 ducks are filling the pond in with their ick. What to do??

In the spirit of permacultural thinking, you need to see how this is a solution, not a problem. You just need to identify what the problem was, for which this solution has presented itself.

My first thought is to see the duck/pond/accumulating-muck location as a new, self-perpetuating system that now supplies you with an unending stream of incredibly rich fertilizer and/or fine garden soil. Just extract it and apply to your orchard, annual beds, accumulate it to build an asparagus bed or some other deep perennial bed, or supplement your soil starter mix.

Depending upon the circumstances of course, most ponds naturally fill in over time. Even small creeks have this happen. A friend in NY with a creek running through his pasture cleans out the creek bottom every few years. Of course the government doesn't want people to do this anymore, but without clearing the bed out,  the creek would naturally silt in and create a bog in the middle of the pasture. This creek is home to plenty of fish and other water wildlife which would cease to be if the creek silts over. I don't know what he does with the dredgings.

I have two small ponds on my farm which accumulate a few inches of muck on the bottom each year. I regularly harvest the muddy muck to add to my garden beds. Rather than leave it pile up yo become a Herculean chore every 5-10 years, I frequently dip a net and take out a 5 gallon bucket of muck. I see it as a resource that my farm provides for me.

Gonna pretty much repeat what others have said:  "Yay, free fertilizer!"

Every year or two I use a plastic rake and a few other methods to muck out my small goldfish pond and use it around plants and in grow beds,etc.

I'll have to do this then. At this point though I'll be using the excavator to muck it out. lol 2 feet of muck in that thing now.

I have two ponds that are quite silted over and have created bogs. Great for wildlife. I am slowly digging them out though as above - great source of good quality soil for my beds as I'm on sand / sandstone.
When digging pond soil out, you to need to move it twice, the first time you leave it adjacent to the pond to allow water to drain out and for all resident creatures to crawl out and find their way back to the pond. Then when it's dry to can move it to it's final location.

I'm hoping to dig out some of the clay bottom to do some wild pottery.

If you have anything below the level of the pond you can use a garden hose to siphon water and muck out using that to irrigate areas that could use the nutrient boost.  Main thing is to do it when you can replace the water that you'll be siphoning out of the pond.