here's another view

picture of fence

overall view

Burning bush does best in full sun and is considered invasive across much of the eastern half of the US......I might reconsider that choice.

Maples are notoriously hard to underplant, so starting with something small initially is often advised. Check out plants that are recommended for dry shade. Not all of these may appropriately hardy for you but check out sweet box (Sarcococca), Japanese laurel (Aucuba japonica), yews, any type of cherry or English laurel (like the Schipka), Kerria japonica, Oregon grape holly (Mahonia cvts).

Pulling the planting area out in front of the maples will increase your choices, both by increasing the amount of sunlight available as well as less interference from tree roots.

"Pulling the planting area out in front of the maples will increase your choices, both by increasing the amount of sunlight available as well as less interference from tree roots." I was going to say the same thing. It looks like there's ample space for a nice, sunny bed, leaving a walkway between that and the trees/shrubs. Then you would have enough light for some larger evergreens, and some more floriferous, smaller plants for summer interest also.