Not a lot of summer and fall shade bloomer perennials. Some of the Cimicifugas bloom later in the summer; the straight species known locally here as Black Cohosh is coming into bloom now. You might want to focus on annuals, and/or foliage colors--blues, yellows, silvers, variegated.

There are two perennials in my partially shaded garden that do really well and are late bloomers. The first is monkshood (Aconitum) which I started from a small clump that I got a few years ago at a plant sale, and it has slowly gotten bigger in the same clump each year. It sends up these amazing deep purple blooms - amongst the very last things in the garden to bloom. And a beautiful native plant which I discovered last year is turtlehead (Chelone). again another late bloomer that has strong blooms right at the end of the season. The one I got last year was pink, but now I've added a bunch in other colours and I look forward to seeing how they turn out.

As to where to get them...local plant sales horticultural groups are the best. Also, buy from nurseries at the end of season (like starting now!) at clearance prices and plant in the fall...and sit down and enjoy the show next spring,

I've found that Aconitum want some afternoon shade, but in full shade they fall over and don't bloom well.

I vote for Ligularia....gorgeous huge dark leaves with tall spikes of yellow flowers..

You have had some nice suggestions for shade-loving perennial flowers. Here are a few more- some perennial geraniums such as G. x cantabrigiense ‘Biokovo’ or G macrorrhizum or G. Maculatum will grow in mostly shade. Several kinds of meadow rue (Thalictrum) are shade tolerant and some species bloom later in the summer while others are spring bloomers. If there are large tree trunks for support, climbing hydrangea is happy growing and blooming in shade though it can take 5 years or more to reach blooming. Native columbine/Aqualegia canadensis will bloom in a lot of shade. Astilbe chinensis blooms in summer here. Not sure when Lamium blooms but it has ornamental foliage as well. For fall, some of the native shade-tolerant asters such as A. Cordifolius or A. Divericatus are worth considering. You might want to consider adding some annuals such as begonias or coleus. Some ornamental colored foliage plants that work in my area include Japanese forest grass/Hakonechloa, Leucosceptrum japonicum 'Gold Angel', Brunnera, Tiarella and Heucherella.

Japanese painted fern, I have several Lamiums that just keep getting bigger & bigger each year..great plant & pretty blooms.