At the risk of sounding heretical, I wouldn't worry about it too much. I garden in a woodland where I get no FULL sun - and there's not much that doesn't grow in my perennial bed. I don't, however, put the penstemons, dianthus, thyme, lavender plants in there - they are on a slope that drains well but still does not get full sun. However, I do have a couple of Saliva greggiis in the perennial bed and they do very well.

Afraid I don't have any suggestions. Have the same situation and have always wanted a showy flowering plant that could tie the whole front bed together. Never could find anything that could both stand up to hot afternoon sun and then flower well behind the trees. So, I focus more on foliage and stem color. I planted some bright striped Carex grass all across that seems to tie things together pretty well. Some hostas (too many deer) and heuchera will go sun and shade but they don't have really showy flowers.