Where is my understory?

My suburban back yard in northern NJ is pretty tiny, around 40’ x 30’.  Between my yard and the neighbor behind to the SW is a band of shade trees.  In fact, this 15-20’ mini “forest” strip bisects the whole block and casts a lot of shade in my yard.  

All the forest foliage is 60+ feet up in the air so at eye level it’s a bunch of vertical trunks.  When the trees are in leaf no direct sunlight reaches the floor, but it is not a dark or dim area – there is plenty of ambient light.  However, nothing grows beneath these trees, except some white snakeroot that had been seeding itself around my yard for 2 years and just appeared in the forest.  There are years of leaves piled up on the floor plus fallen branches and trunks.  I’m so inexperienced I don’t know whether to consider this area poor & neglected or healthy & pristine.  I also wonder why there is no understory – no bushes, forbes, etc.   Perhaps the deer that go through there eat anything that tries to grow.

Anyway, I’d like to have a mixed border of native shrubs along the back of my yard to provide a sense of enclosure and food for wildlife.  The previous owner of my property had planted a hedge of lilacs and forsythia all around the yard, right on the property line.  Along the back edge they grow SIDEWAYS for 7 feet to what I’ll call the inner border that gets a bit but not a lot of direct sun.  There they branch out very sparsely to form a scraggly balding hedge.  He had even tied the bushes to iron stakes in the ground to hold them at the edge, but the plants pulled the ropes loose and stretched horizontally to the inner border.  Clearly, they are reaching for sun, and the very same plants do just fine and grow upright on the less shady side borders.

Forsythia & lilacs are rated for full sun.  I’m wondering if I replace them with woodies rated for shade will the new shrubs also grow sideways or upright?  In a perfect world, I’d have a screen of mid-high shrubs & understory trees in the same spot along the back edge, fronted by something like hydrangea along the inner border.  If I place the screen at the inner border then I’m shortening my already small yard and forfeiting at least 7’ of land.  

I should mention that all the forest trees are on neighbors’ properties, none on mine, so cutting or thinning them to increase light is not an option.  And even the inner border along the back is part shade at best.

I’d appreciate some advice from more experienced gardeners.

Not only lack of sunlight for plants is an issue here, but also moisture. If you've ever stood under a tree during a rain shower, you're aware that a lot of rain doesn't make it to the soil. And what does reach the ground often is greedily sucked up by the tree's surface root system. So lack of both sun and moisture contribute to why little grows directly under a tree. Add to that a thick layer of old tree leaves, even weeds have a difficult time pushing through that mulch. Just think of it this way, gardeners often use a thick layer of leaves to prevent weeds from sprouting in their gardens. It can be quite effective.

But if one chooses the right plants and puts a little care into it, one have have a nicely landscaped area under trees. I used to live in South Jersey in a heavily treed area of the Pine Barrens. My front year was carpeted in greenery under the tall oaks and pines. Wintergreen. Sheep laurel. Azaleas. Rhododendrons. Hosta. Assorted ferns. There are other shade loving plants but I don't recall offhand what else I had. A high quality nursery could help you with your choices.

Lots of words, often it is good to put some pictures in - I know the technical hurdles ....
Of course we all love trees but sometimes you can only get a productive garden if you cut something down or at least thin or cut off some branches (your neighbours trees seem to be a bit high to comfortably cut away brances).
I don't know about your climate but in my climate I would put the chicken in there or at least a part of it and the other part maybe for growing mushrooms?

I appreciate the responses.  Listened to a Cornell lecture about Forestry and I now believe the mini-forest is bare below primarily because of the deer.  Not a worm invasion since the leaf litter is there, and not invasive plants.  So in addition to worrying about sunlight I need to consider the deer as well, lol.