I had love in the mist in a slightly damp spot in Launceston and they self seeded. May not work if too damp. May be worth a packet to see how you go. Sorry not to be more help.

There are a group of Irises - Louisiana Irises I think they are called that love wet feet.

Shaded all the time...

Have a look around for Saxifraga wada. There are several sorts. They have dark leaves and small autumn flowers which are attractive.

On the edge of the 'wet' zone you could plant Iris gracilipes, which is a little woodlander that flowers in spring. Likes a topdressing of humus in autumn.

Corydalis - the blues and creams. They need a bit of sun - dappled or direct for some time in the day. Spring flowering.

Hostas - plantaginea has scented flowers and sieboldiana has huge bluish leaves. You can do dramatic things with them. Summer to autumn flowering and leaves.

Colocasia and Alocasia aka elephant's ear - they die away for winter but will be back in spring. Huge and lush but flowers aren't much.

Natives - Dianella? Some of the ferns - especially the filmies (yum!) Some of the orchids?

If you're feeling brave - the big 'Green Goddess' Zantedeschia. But they can be weedy...

Impatiens, although they do like a bit of sun to do well. Also Anchusa (mind the bristles) and some of the asiatic lilies. Astrantia and Tolmeia. Begonias. Clivia-go for little plants and feed them up if they cost hideous sums. And you might want to check out some of the bromelliads with brightly coloured leaves as well as flowers.

If you have some 'light wells' in the canopy you can probably do a bit more for a few years, until they fill in again.

For the really damp part - a 'zen' type garden with lovely rocks and mosses/ferns? Not flowers, I know.

For bulbs, the Earlicheer narcissus are pretty water tolerant, but they will need light - at least six hours a day.

Certainly don't try and grow Louisianna irises in Tasmania - too cold. You will get plenty of leaf growth, but not much in the way of flowers.