I don't know of any evergreen azaleas that will bloom reliably in dense shade. The best azaleas for shady areas are deciduous azalea. Here are some:

Rhododendron calendulaceum, the flame azalea, is a native American species, growing 4 to 6 feet high. It bears clusters of 2-inch clove-scented yellow to red-orange flowers in early summer, when most other azalea species have finished blooming. The leaves are 3 inches long and drop in the fall. Does best with partial shade.

Rhododendron kuisianum, the Kyushu azalea, is a low-growing Japanese species, only 18 inches high. Its leaves are deciduous when the plant is young but evergreen in maturity, remaining on the plant all winter, though often changing color. In its original form the Kyushu azalea is covered in mid-spring with 8- to 10-inch clusters of lilac pink flowers, but there are many named hybrids derived from this species. It prefers partial shade.

Rhododendron schlippenbachii, the royal azalea, is a deciduous species, also of Japanese origin. It has soft green leaves that grow in whorls around the stem and turn yellow, orange and crimson in the fall. Its pink star-shaped flowers bloom in loose clusters in mid-spring and have a delicate fragrance. It needs shade from hot sun. Dappled shade or morning sun/ afternoon shade is necessary to protect the rather thin textured leaves from scorching.

Hybrid deciduous azaleas: Most hybrid deciduous azaleas do well in full sun and frequently are poor bloomers in the shade. "Maid in the Shade" deciduous azaleas is a collection of deciduous azaleas compiled by Transplant Nursery selected to do well in shadier locations. They include:

* 'Summer Lyric' - Flowers are a mix of pink with yellow throats.
* 'Lisa's Gold' - Golden-yellow flowers.
* 'Camilla's Blush' - Blushing pink blooms that hummingbirds find irresistible.
* 'Kelsey's Flame' - Bright yellow and orange flowers.
* 'Lavender Girl' - Pale lavender flowers
* 'My Mary' - Pale yellow flowers, named as a tribute from George Beasley to his wife Mary.
* 'Rosy Cheeks' - Dark rose flowers with golden throats. Its fragrance can rival that of a rose.
* 'Nacoochee Princess' - Regal white flowers that are tinged with pink.

Here is a link that might be useful: Rhododendrons and Azaleas For Shade

What about a substitute such as Illicium henryi or floridanum? These are evergreen, produce masses of pink and red blooms around azalea season, and seem to thrive for me in deep shade. As a bonus, their drainage requirements don't seem to be as stringent. Henryi seems to flower in deeper shade than floridanum, and it doesn't share the mildy annoying habit of having its old foliage yellow and fall off just as the blooms are at their peak, at least in my experience.