I read that huge Camellias are growing in filtered pine shade in China. Locally, in our filtered pitch pine barrens shade, we have huckleberry (Gaylussachia sp.), partridgeberry (Michellia repens), blueberry (Vaccinium sp.),mountain laurel (Kalmia latifolia),sheep laurel (Kalmia angustifolia),wintergreen (Gaultheria sp.),and any number of rarer and more difficult plants like Conradina,Pipsissiwa, trailing arbutus and sand myrtle, where patches of sun get to the ground, so your choices seem vast. I also grow Asarum europeaum and Epimedium easily here in my acid soil, as well as Azaleas like 'Flame Creeper, that are, practically, ground covers.
Check out, locally, what is growing in the arboretums,parks and woodlands in similar conditions to yours.

First, decide which areas will be shrubs/flowers/ferns, etc., and which will be grass/lawn. The grass areas should be raked free of pine needles, loosen the soil with a hoe, and this month you can plant seed.

You can rake the extra pine needles and any leaves that fall onto the areas you want to grow shrubs, ferns, and flowers. Lots of shrubs, wildflowers, and ferns should thrive in part shade. Look around your neighborhood for plants that seem to be doing well in settings like your yard. Look in nearby woods to see what types of wild plants do well. Once you know what to look for, I bet you can find cheap ways to obtain plants. Many plants are easily divided, and local gardeners will probably be happy to give you pieces of their plants - just walk around the neighborhood and ask questions. Garden centers, Home Depot, etc. may have plant sales going on at this time of the year. This is a great time to plant shrubs and some perennials can be planted now as well.

I wouldn't worry too much about the clay soil. The soil in the rest of the neighborhood is probably similar, so plants growing nearby should do fine in your yard, too.