Illicium floridanum & I. henryi do well in moist shade.
Illicium floridanum pics.
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I. henryi pic

Although needle palm (Rhapidophyllum hystrix) does well in light shade, the north side may be too windy for this shrubby palm. However, I do grow needles in the open. Hardier varieties of Camellia japonica should do well. Stop by Triple Oaks & pick up a Tetrapanax 'Steroidal Giant'. Also consider Daphne odora & Edgeworthia papyrifera.

Daphne odora

needle palm dusted with snow

If you like the tropical look, you might consider Acuba japonica, Camellia japonica, or even Fatsia japonica on that north side. Palms are great for a tropical look but that hard northern exposure is not really for them--Needle palms need that high summer heat as a southern exposure would provide, and Windmill (Trachycarpus) palms would appreciate more protection from cold northern winds. Also, don't neglect ferns--they are amazingly tropical looking and some are evergreen even in the North. Oh yes, you might also consider a non-running/CLUMPING bamboo. Fargesia rufa does well for me in a heavily shaded eastern exposure. If you buy one plant, you can divide them yearly to make a hedge. I did it that way to save money--they can be costly but are worth it in the proper environment.--DO NOT put a 'running' bamboo there (any of the Phyllostachys for example) or you WILL BE SORRY. Good luck.