Mugwort (there are a few species with that name, two of them are very aggressive invasives) is devilishly hard to control, so this is not going to be an easy task. I am not a fan of careless herbicide use, but a large monoculture of mugwort is one time I would consider its use.
Hand-pulling is probably not an option with a lot that large except for isolated cases (which I explain below); that would be an incredible amount of labor, especially since with mugwort you need to dig deep to get out rhizomes, and still need to come back multiple times.
Probably your best bet here is a combination of competition from aggressive native plants, and avoiding disturbance that favors the plant. Mowing tends not to harm mugwort very much. Tilling tends to actively favor it. So the most important thing here is to avoid tillage or any sort of major soil disturbance.
As for competing grasses, if you have a silt loam, you might have the best luck with big bluestem (Andropogon gerardii); that species prefers, and is most dominant on silt-loam in bottomland areas with abundant moisture, and if this area is near a pond, you probably have just the right conditions for this. Another grass that can be pretty aggressive is virginia wild-rye (Elymus virginicus) and I would also include indiangrass (Sorghastrum nutans) and switchgrass (Panicum virgatum) in the mix. Those grasses all have good ground-level shade-tolerance and ability to compete against herbaceous vegetation. There are all sorts of other grasses you could try throwing in the mix too. Two of the annual Panicum species, Panicum capillare and Panicum dichotomiflorum can be good to throw down on areas where the soil has been disturbed, if you already have some exposed soil and you want something to compete rapidly with the mugwort. Also consider purpletop (Tridens flavus), yet another grass that might like your conditions and be fairly competitive.
Also look into aggressive broadleaf plants. You're kind of at the edge of its native range, but you might have good luck with false sunflower (Heliopsis helianthoides) which is tall enough to compete favorably with mugwort. Also get goldenrods in there. The most aggressive two are usually Solidago altissima and Solidago canadensis, or in moister areas, Solidago gigantea which has higher water needs but gets even taller; they're also all powerhouses at supporting biodiversity. And consider some asters; frost aster (Symphyotrichum pilosum) might be a good one, also New England aster (Symphyotrichum novae-anglicae) for more average conditions, or if it's very moist conditions near the pond, white panicled aster (Symphyotrichum lanceolatum). All of these are tall-ish and can be competitive with mugwort. Try milkweed, common milkweed (Asclepias syriaca) is probably best, or perhaps swamp milkweed (Asclepias incarnata) next to the water. Milkweeds can germinate and establish in the fall so they are also a good option to seed in if you have any exposed soil late in the growing season.
Although mugwort tends to be resilient to mowing, you might want to start off your project by trying to mow the mugwort repeatedly over one season, during the growing season, to stunt its growth and deplete its energy reserves so it will be less competitive the following year.
Keep in mind though that mowing later in the season will allow winter annuals to establish. In agricultural and/or suburban areas, most winter annuals are non-native and many of these will persist late enough into spring that they can inhibit the germination of native plants that you have seeded into an area. Ideally, you want to carry out your last mow some time probably in spring of the next year, shortly before the time when you want the new seeds to germinate.
I also recommend making this an ongoing project. "One-and-done" interventions for controlling invasive plants rarely work. You may need some trial-and-error. Some plants you try to get established make take and may compete favorably, others not. You can also experiment with small plots and then figure out what works and then carry out that same scheme on a larger scale.
In the medium-run, I would not just stop at an initial seed mix. Go around your area, and look at what native plants you can find. Gather seeds and seed them into your field. And even if you don't have the labor resources to manually weed the whole field, you can still do some powerful spot-weeding. If you see an area where the mugwort is competing against some native plants, go and pull those ones. If there is a spot where the mugwort has a monoculture, mow or weedwhack it. If a new isolated mugwort plant comes up in an area where there isn't much of it, pull it and dig out the root as best you can. Try to focus your effort and resources on the places where you will be getting the most benefit. Ignore areas where the native plants are doing well. You would be surprised what you can achieve with a few hours here and there, if the work is targeted on the areas where there is the most competition. With time, the native plants will gain the upper hand.
In the long-run, in your region, bottomlands with silt-loam would have grown up into forest, so you might want to look into allowing your land to follow a natural succession trajectory and grow up as forest. There is not a lot of intact forest left on Long Island, on loamy soils, because most of the land is coarse sand left as glacial outwash, and the few remaining loamy soils are mostly developed as suburb, or still in use as agriculture. So, allowing forest to grow up here would provide a habitat that is high value and rather rare in your region (most of the forests remaining on Long Island are on sandier soils.)
