I had paperbark birch seeds, which are also pretty water tolerant (though not as much as river birch), but none sprouted - ironically I think the seeds were too wet when I stratified them (same with my maples). Isn't river birch (B. nigra) a warm-weather birch species? I've got some cuttings of random local birches from a neighbor but I have no clue whether any of them are water tolerant enough to take swampy ground. Also birches don't usually get that tall so I don't know how expansive of a root system they'll put down. The abundant local species B. nana (dwarf birch) grows (nay, volunteers) readily here almost anywhere that sheep don't graze, but it's just a shrub, I doubt it'd do the trick (though it's probably better than just grass). It can take wet soil, although not totally swampy conditions.
For the wetter areas I also have about a dozen or so western redcedar seedlings - they're not as swamp-tolerant as dawn redwood and western recedar, but they're still reportedly quite tolerant of wet or even waterlogged soils, and they should be more cold/wind hardy than those two (wind is actually the big issue, it doesn't really get that cold here). I've also got a number of other pacific northwest trees with varying degrees of standing water tolerance. Oh, and a species or two of tasmanian mountain eucalyptus (don't remember which ones) that tolerate fairly swampy ground and should at least stand a fighting chance against our winds.
Basically, I'm just going to plant a ton of stuff and see what survives. ;)
One plus is that where the ground is persistently wet and at landslide risk, it is slowly flowing water, it's not standing. It's constantly replaced by fresh, cold ground-filtered water, so there's probably not as much risk of root rot as might be common otherwise. But there's still the oxygen issue. That and the damned sheep, but I'm working to fix that issue once and for all...