Thanks! I got a 330gph pump and filter, got the whole thing installed today, and cleaned out yet more debris from the bottom of the pond (four pine cones, and a small tree's worth of leaves). I can actually see the rocks that are down there now, a first since we moved in! The water is finally clear enough that I can actually see the stuff that still needs to be pulled out, which is a refreshing change from where I started, and hopefully the new filter will pull some of the muck instead of letting it just settle back to the bottom. Four years of neglect is a lot to compensate for, though. I also got a better count of the fish and it appears we have 19.The rule of "Half The Pond Volume Flow Per Hour" I would argue only stands true if your pond is 1,000 Gallons or more. The smaller the body of water, the more circulation it needs, the more aeration it needs, etc. If you had a 4,000 Gallon Pond, then a 2,000GPH pump would be fine, for you I would say at least 500gph size pump is the way to go. My pond is the same size as yours at 500 Gallons and I run 950gph and 650gph pumps 24/7 because that is what I was taught on here and what has worked for me since. I would say your 250gph UV clarifier is fine, just add another 250gph stand-alone pump to the pond, maybe with a Spitter to help aerate more, Plus it's always good to have 2 pumps in case one goes out!
I did what I estimate to be about a 35% water change over the weekend, and plan to do another one this weekend. I was working in the rain or I could have done more. I will get a photo once things settle back down out there. Up until now I was way too embarrassed of how it looked to post one. It's still not in great shape, but progress is being made.