I'm back in town and frantically trying to catch up on everything. (You'll like the photos of the garden I visited, but I haven't had time to load them up yet.)
I've been thinking about your under-the-shed tree, and I'm now leaning towards sourwood. I was originally looking for something with alternate leaf arrangement with an entire margin, but nothing matched the size and shape of the leaves and overall habit. It's possible the slight rippling on the leaf margins is actually masking a fine serration. Take a close look at one of the leaves and see if it is serrated. Compare to photos of sourwood -Oxydendron arboreum. Persimmon is another possibility.
