Here is a garden under an ash tree in OH in it's even though the garden was just over a year old at the time, from previously being sparse grass. There are hostas, columbine, creeping phlox, Pulmonaria, Bergenia, Trillium, violets, Polemonium (jacob's ladder,) a few bulbs, Lamium, a little lilac, ready to be a tree if the ash got emerald beetle borers (I moved, remains a mystery,) and a few others I don't remember and can't see from this angle. 4" of mulch can retain moisture for weeks. Of your list, I would avoid the Vinca. Just too sprawling/spready to play nice with the other plants. In general, you don't want vines in a flower bed. Entities like Vinca or Ajuga that rapidly spread really do best in their own, well-enclosed space. Spreading through other more self-contained plants, these spreaders can make the whole thing look like a confused mess. But, like most things-gardening, this is subject to your personal opinion on the matter.

May I take the time to explain that the roots do not need sun. It is the leaves that need the sun light for photosynthesis. Our zone is very challenging to even find a cane hardy climbers. That said they would need 6 hours of sun to bloom well and be a robust grower. They would also need support for you to tie them to as roses do not naturally climb. If the arborvitae is east then this is a northern exposure correct. A clematis will mature much quicker than a climbing rose. Roses tend to take a good three years of building root mass before they show what they can do. Here is a photo of Dortman at Cleveland Botanical Garden posted by Karenforroses. At the top of the page you can search previous posts on here. Just type in climbing roses for zone 5. or Hardy climbing roses zone 5. Each time you change the words around you might get some different post. Lots of good ideas in those older posts.

Knowing where you are (zone 5 is vague) and having a pic (or at least the dimensions) of the area would help. Also, this isn't a very active forum so try posting this in the Shrub Forum or the Perennial Forum. tj

I have a red twig dogwood in very deep shade. It is about 8 feet tall. It has never flowered, but is doing fine. Of course it is deciduous.