Not evergreen, but Clethra alnifolia and its numerous cultivars would love to be in a moist shade. Very fragrant. Bloom time July to September depending on cultivar. Expect it to be 6-8' tall in 3 years if you plant at least 2 footer.
Kerria Japonica is highly adaptable to any conditions and will bloom in almost full shade. Stems stays evergreen year around. Bloom in early spring right after forsythias and rebloom (if in sun) in August. Expect the same 6-8', but stems are slender and may spill/droop on your staircase.
Both plants will produce suckers in moist conditions, but they are not spreaders and could be easily controled

Evergreen and wet .... see if Florida anise (illicium floridanum or pavriflora) is hardy for your area. Another choice is Inkberry, Ilex glabra.

Illicium floridanum didn't do well for me.
No, it didn't die completely, but was so ratty looking after not so cold last winter, that it had to be discharched. It was planted in protected site where most of z7 deciduous plants do well, not evergreens.

I have a Nandina in my shade garden, next to the faucet as well. It's quite shady, but has not gained the height you are looking for. It's about 4' now, but sort of delicate looking and does not retain it's leaves in winter. Kind of looks like a twiggy stick in the snow.
I do LOVE my Clethras!!

Clethra...is that evergreen? How tall does it get?

Clethras.
Link is below.

Here is a link that might be useful: Clethra alnifolia

Itea virginiana - Virginia sweetspire - is semi-evergreen in zone 6. Mine keeps its leaves until January or longer. And it does fine in moist shade.

I've had good luck with Rhodendums in moist shade in Z5. Maybe it is just a fluke but I have one doing fabulous in an alcove right by my ever dripping faucet. I do buy the larger pots rather than the smaller size plants which might be a factor for their success under those conditions.

It depends on how shady and wide the site is. Besides the shrubs already mentioned I vote for Fothergilla major. Hydrangeas are nice too.

Itea virginica - also has great red fall color.

Susan

Itea in shade doesn't develop good fall color, at least here in New England.

Mmmm. Does here in OKC - maybe because we are warmer than you???

Susan

I planted a itea virginica (sweetspire) this spring in a spot that gets morning sun, afternoon shade. Did well and is turning red now. Seems to be doing good in that spot.

Another vote for sweetspire here. Its nice to find things that bloom in August when so much of the garden is in a doldrum. Fragrant white flowers.

Itea in August?
I'm in a colder zone than you, but it always done fore me by the middle of July, sometimes even earlier if spring is warm.
Then clethras starting to bloom, species being the first and 'September Beauty' the last.
I do agree, though that for fall color not many plants could rival Itea, but...to get that show you have to plant it in more or less sunny location, not a shady one.

Aucuba is evergreen and loves shade and moisture.

I can highly recommend Leatherleaf Mahonia. I hated it when I first moved here, but grew to love this plant that grows in an area that some years doesn't dry out in the spring. The leaves turn red and drop off when they get too much sun. The real glory is that it blooms in January and my porch light picks up the pale yellow flowers in the evening, glowing in a sea of dark foliage. The dark blackish green berries that follow are nice, too.

The only con is that the sharp leaves are nasty! Plant under the window of a teenager if possible. :D

I have a Rhododendron Catawbience (sp?) and an oriental azalea both growing in most shade that are doing very well here in NY.

Penny