Where is the pump pulling water from? Is it in the mud? Silt can be from run-off of dirt entering after rain. Maybe move the pick up for the pump (not familiar with your setup) or create a plastic box/bin or use a 5 gallon (drill a ton of holes into it) with a lid, and line it with the porous foam strips meant for gutters to keep leaves from getting in the downspout. I've used those in a 5 gallon with high volume sump pump and flow was uninhibited. Did this to distribute suction over entire 5 gallon vs. a single 2" pipe inlet to avoid clogging could probably be a decent pre filter though I've yet to install one on my pond pump.
I'm gonna say 1" isn't enough or you wouldn't be having a problem right now. For what it's worth, I have somewhere between 15k and 20k gallons in my pond. I didn't want to mess with a bog either. Currently using a single 55 gallon food-grade barrel. Ran 2" pvc into the upper side area of barrel, created a spray bar (it's not pressurized, but distributes the flow evenly) to do a top-down deal. Cannibalized an old reusable home furnace filter (very thin, fine-hole vinyl screens and a 1/4" foam sheet; filter frame unscrewed apart) and running old pillow poly fill (one pillow worth; I split the polyfill down the middle, so instead of 8" it like a 4" mat if dry). Basically the vinyl screens + 1/4" sit atop the polyfill to protect it from spray bar. Poly fill sits atop aluminum screen which is wedged into the barrel. Below aluminum screen is another screen with sponges evenly laid out (the blue scrub type; cheap porous sponge disintegrates into globs; guessing bacteria eat it) and sandwiched together. Very bottom is lava rock. I opted to run dual 2" outlets a little over a foot above bottom, and have 90 degree turn downs facing down, so water has to actually rise to exit. Pump is a technically too small for the size of the pond, but is a 4500 gph harbor freight pump with FULL 2" threaded into it and feeding filter, running 24/7. Dual outlets help the water exit quickly w/o backing up. Seems to be a good balance.
About 1/3 of the pond is between 2' and 3'. Deeper end near center is over 10' with a sump hole around 12'. Pond gets full sun from around 10 am to sunset. Water is perfectly clear. Heavy rainfalls (like 1.5" in 15 minutes, which is now apparently the new normal this summer) take about 10 to 18 hours to clear up. No algae. Plants are thriving. Have around 15 resident green frogs (2nd run of late season tadpoles presently; earlier season of numerous types of tadpoles already climbed out to the lily pads, then eventually left), tossed in a few dozen bait shop, fathead minnows several weeks ago (more babies than I can count right now, easily in the hundreds, and various sizes from just born to about 2 weeks old maybe) and guessing about a dozen survived the transplant (they hide in the rock gaps and are hard to see even when swimming so hard to tell) and apparently have been spawning like crazy with the warm water given the various sizes of minnow fry now.
That polyfill on my setup is what gets the dirtiest as it's catching everything. I lay it out on a stretched aluminum screen section, then spray it with garden hose (have good, untreated well water at the spigot so can actually do that). Have a drain valve with 3/4" hose barb at very bottom of barrel if needing to drain.
My set up works and is contained to a small area of the pond right now. Everything in the pond seems to be healthy so far this year. Rain water keeps it topped-off; untreated well water via sprinkler when long periods of no rain to add 1 to 2". If wanting to do a waterfall feature, I could always run a second, small $25 pump to recirculate water to the feature area, hide a custom spray bar, etc., or relocate the barrel to exit (in my case, too much risk of water leaving the pond) there instead.
Anyhow, there's more than one way to filter a pond. Consider adding some poly fill if possible. If your setup backs up, it either can't get the water out fast enough, or possibly the filtration media is too compressed under the weight, too dense, holes are too fine in the foam, etc..
