SD,
Hi there I had several posts on "rust colored flat worms" (you should find and read) and came up with many good suggestions. My tank at the time was a 12 gal nano-reef. To be clear my flatworm problem involved tiny rectangle shaped, rust colored worms with a tiny red dot in the center (very flat), and they would move around the tank depending on current. They really began to cover vast areas of my tank, and I have heard that they can even cover corals and starve them of light (not in my case however).
What I did: siphoned thousands out for days at a time- they seem to come back even stronger. Gota arrow crab- only ****ed off the rest of the tank, no worms eaten at all (that I could tell). Got a six line wrass-what a cool fish but he didn't touch a single flatworm (that I could see, problem getting worse). Tried to vary current to get them in one area for easier siphoning, that worked a bit but every time I removed them, they seemed to come back and multiply even more! Like you I wanted to avoid chemical treatments at all costs but when they really took over I finally broke down and got the Flat worm Exit. Very easy to use, follow directions exactly and it will work (at least it did for me). I put in the FWE (as directed) and almost immedialtly most of the worms were dead. I also took it one step further and set up 2 dips in 30 gal rubbermaid containers-one with SW (same as my tank) with FWE in it also, and one with clean SW (to shake off rockwork vigorously to get the dead ones in the rock off). So I first treated the tank(30-45 min), then I pulled out all the rock put it into the second tx container (shook the rock real well) and let it sit for another 30-45 minn and then I put the LR into the 3rd clean SW rinse (no FWE) and shook the rock again, then before I put the rock back in I stirred up the sand bed thouroughly to get other Flatworms up, put fresh carbon in and then put the LR back in the tank. Bye the way in my tank durring treatment were some green mushrooms, feather dusters, cup corals, and clown fish a cleaner shrimp and a diamond goby. I checked back over the next few days and found a few more live flatworms (very few) and will treat the tank again soon (as per directions-you are supposed to tx 2-3 times I believe). That was over a week ago, and all critters look fine (no problems yet). Post another time if you want me to check back and let you know the ongoing prognosis and I will do so. Just read and follow directions carefully. Good luck with that. Also be aware that the Six line Wrass is a very delicate shipper so if it looks bad in the store wait until it gets better there before you take it home.
BB