Wow! Very challenging!
All those things you put in the title, heavy shade, shallow soil, subject to freezing make a tough growing environment. But then add in the pond liner and it is kind of a disaster. I take it this very large planting box (4 by 20 ish ?) is outside, where it gets rained on? It will fill up like a bath tub and everything will drown. Hmm, you said that it is part of a covered entry way. Does that mean it does not get rain? That is a help for the water issue, but you still have to water the plants.
People always used to put gravel (broken up pots, small rock, etc) in the bottom of flower pots, thinking it would aid in drainage. It does NOT. And especially where you have so little room for soil to start with, the rock just takes up space that could be soil. Water does not cross the dividing line between the soil and the rock until the soil is completely saturated. Please do read this short article about stone in the containers as a garden myth and why: https://www.todayshomeowner.com/garden-m ... ontainers/
I think you will need to look for bog plants, things that can tolerate standing water or saturated soil, like: lobelia/ cardinal flower, bog bean, marsh marigold, obedient plant, white pickerel flower, milkweed/ butterfly flower, thalia. None of those are evergreen. For something evergreen consider:
Atlantic white cedar (Chamaecyparis thyoides "Shiva") is a dwarf evergreen that thrives in a soggy spot and grows in U.S. Department of Agriculture plant hardiness zones 3 to 8. Light greenish silver needles turn to a bronze shade when cooler weather arrives, and small rounded cones develop in the spring
Consider the shrub variety inkberry (Ilex glabra), which grows in USDA hardiness zones 2 to 11, to 10 feet high and wide, with dark green leaves and black berries. Dwarf varieties are also available and are suitable for creating low hedges. Yaupon (Ilex vomiitoria) grows to 20 feet high and 15 feet wide and tolerates high alkaline soil. The dwarf variety grows to 5 feet high and wide and both grow in USDA hardiness zones 3 to 9.
https://homeguides.sfgate.com/evergreen- ... 28382.html
Here's an article from Penn State about trees, shrubs, groundcovers for your area that tolerate wet soil: https://extension.psu.edu/plants/gardeni ... -wet-sites
You would have to investigate them for which ones also tolerate shade.
Part sun is one thing, but deep shade is pretty killer. Of their list shade tolerant ones include sweetspire, button bush, summersweet, leucothoe, swamp azalea, lady's mantle, plumbago, bleeding heart, daylilies, hostas, pulmonaria/ lungwort, tiarella/ foam flower. The leucothoe is a very low growing broad leaf evergreen that might be worth your consideration.
But shade tolerant does not mean they would thrive with no sun. Given how many other challenges this area has, have you considered adding some artificial lighting to help your plants along?