I hunt a marsh area that is much smaller, but the exact same kind of thick brush. Some of area I hunt is wide open, so that actually helps the deer move through certain areas. I am also lucky to have a couple trees, and by a couple I mean 3, that I can put stands in. I also use a tripod stand and a popup blind. I'm not sure what your terrain is like, but I will tell you how I hunt mine, maybe it can give you some ideas.
There is a small patch of brush, no bigger than 50 yards by 50 yards, right by the edge of a large open area that grows up with tall marsh grass and wild rice. does bed down in that patch of brush, and I hunt the edge of that brush where they come in and out. especially during the rut, bucks will cruise past this small brushy area wind checking for does.
There is a ditch bank that makes a horseshoe shape pattern just inside the actually property line. with the lay of the land, there is a stretch of ditch bank about 400 yards long that helps form a funnel between two wet areas. this funnel area runs the length of the ditch bank, about 400 yards, and is about 50 yards wide, running between the ditch bank the some higher ground near the property line. There are some open areas in the thick brush where trails cross, I hunt those open areas with the popup blind.
The other thing I have done is blaze some trails in the brush. the deer go everywhere and anywhere in that kind of thick cover, as I'm sure you know. i'm lucky to see the same trail be used more than once because there are so many trails. but after hunting my area for a few years, i've learned the general direction they move. they love moving through that funnel area, moving parallel with the ditch bank down in the thick cover. in some spots I have cleared some long lanes for shooting that cross some of the heavier trails. rattling and grunting works fantastic for me in this swamp, the hard part is keeping the wind direction good. since they can and do go everywhere, it is almost impossible to keep them from getting down wind. the best i hope for is to watch down wind and hope i get a shot before they get all the way down wind and smell me.
its a real crap shoot, hunting marsh areas is very difficult. i like to get up in the tripod stand whenever I can. i get it set up and trim some shooting lanes. the popup blind comes in handy too, gives me the chance to move around a bit. if i find an area i really want to sit, i just set up and cut a lane to shoot, thats about all you can do in such heavy cover. i try to hunt the few open spots that are naturally there when i can, but that doesnt always work. but after a few years, i have learned some of the more main travel patterns and have been able to concentrate on being set up around those spots.
hope this helps a bit, its hard to explain well without showing you a map of the area i hunt and how I hunt it. the first couple years I didnt do very well, but once I figured out where the deer were moving, I was able to start getting some shots. good luck.