That sounds like you have an awesome situation on your property. Should be fun to work on improvements over the next several years!
You can filter out sediments from the swamp. However, you cannot "filter" out tannins, nitrogen, or phosphorus.
You need rooted plants or algae to take up (utilize) the nitrogen and phosphorus. (I am not sure about the tannins, but since they are organic compounds, I suspect they would also be taken up by photosynthesizing organisms.)
Since you don't want your nitrogen and phosphorus to grow algae in your lake, then I think rooted plants are your best option for "cleaning" your incoming water.
There is already a culture of people that perform that process, but they do it on a slightly different scale from your proposed project. However, I think you could utilize the same principles.
They do something called "living pools", where they try to create clean, clear water by only using plants to do the work.
Living Pools article(Once you start searching on that topic, I suspect you can find much better articles than my link.)
I think you could utilize plants that do well in your area, that are placed in your created pools and channel ways. Maximal water travel distance would be your goal, so your swamp water has the most "residence time" among your plants before entering your lake.
You must also have a way to cut and clear your plants during the year. The grown vegetation must be removed from the watershed basin to also remove the nitrogen and phosphorus that ultimately came from your swamp.
You also need to be careful to pick the right plants. There are plant threads on Pond Boss that discuss plants that spread rapidly from seeds or even broken pieces of the rooted plants. You do not want those types of plants colonizing to your lake!
I hope the gives you a few ideas. If you ever get to the point of choosing specific plants, start a new thread and some of the experts can give you some good advice.
P.S. Some types of fish prefer moving water (streams). If you did create a good network of pools and riffles, would there be a type of trout you like that would thrive in those waters? I don't know what your minimum daily water throughput would have to be, but I suspect you could at least support some small numbers?
Good luck, and have fun!