The Cleveland seems to suffer less from the same structural problems as the Bradford, but is as capable of being invasive, so I suggest that you look further for a tree. If you only have 6' of kitty-corner distance, if I am imagining the space correctly, then you really want a narrow tree, that won't get over 12' in width, to fit in the triangular area between the barn and the ramp. Is the ramp in frequent use? If so, then you will need to be careful what you plant so the access to the barn isn't hindered. You can do judicious pruning and limbing up as the tree grows, but still, the less work, the better. What about a single trunk - or only 2-3 trunked - Amelanchier/serviceberry? It throws light shade, and, depending on the cultivar, is more or less native, and tough. Redbud is another possibility, although the shade may be too heavy. Hawthorn, especially one of the natives, might work, although if the ramp is in use, the thorns would be a no-no - I THINK there may be thornless selections. But if fireblight is common in your area, forget it. A selected crabapple might be good - they are pretty tough, and some are less spreading than others. Another possibility might be Chionanthus/fringetree. A taller viburnum, with careful limbing up as it grew, might work. Lilacs, with control of suckers, might also work.

Calliope -- I winder why your Serviceberry has no fall color? Oh, it has but they can go any shade from yellow to gold to red. Mine is a very light gold with a watery red wash. Not what I'd call very spectacular, especially if you consider its delicate and open structure, smaller leaves and the riot of the display in the trees around it like vibrant gold ash and the gaudy red of the acer rubrums. Shadblow is a very 'natural' looking tree. It certainly looks like nature stuck it there and doesn't have the 'in your face' looks of many ornamental cultivars. IOW not a tree I'd plant where it has to be the center of interest if I had other choices. The leaves on mine tend to drop early too compared to many around it. Mine is almost bare by now, one of the first ones to shed, actually in that area. Great to carry off a naturalistic theme, however. The berries are over-rated too compared to other trees I plant for wildlife.

I live in the Carefree/Cave Creek area and have nine mastic trees of varying ages on my property. I love them. Believe it or not, those that have done the best came from a Lowe's plant nursery. Although some commenters above have stated that mastic trees are true evergreens, they nevertheless do experience some leaf loss at this time of year (March and April), but it is no where anything like that experienced by deciduous trees. The first year that this happened with my first mastic tree I became alarmed that the tree was in a state of collapse, but this turned out not to be true, especially in light of the fact that it also was pushing out bright new green leaves. All nine of my mastic trees are currently experiencing some minor leaf loss of older leaves while putting out new healthy growth, so I have to assume this is normal. Although mastic trees are generally drought tolerant, they require some coddling for the first year or so until they are established. For the first two weeks after I plant a mastic tree, I water it every day in the morning. Then I go to watering every other day. When the really hot weather comes in I go back to watering every day until temperatures moderate in the fall (established trees don't require as much water). As fall progresses I water once a week for all trees, then every three weeks during December and January. Even though we had a few occasions this past winter when temperatures dropped below freezing, my mastic trees showed no ill effects. And, as the days got longer and the weather warmer, they put out lush new growth. The photograph shows a mastic tree that I bought in a 2-gallon container in December 2013 for $19 at a nearby nursery. When I bought it it was more of a bush than a tree, but I found one stem that could serve as the main trunk, so I am training it to grow straight using stakes I bought at Home Depot. Its height is now 64 inches. In the background along the cinder block wall are three mastic trees that I bought at Lowe's in January 2015. They are growing beautifully. All of these mastic trees pictured get morning and early afternoon sun, but a large mesquite tree to the left of these trees and not seen in the photograph later provides shade as does the cinder block wall and the house next door as the sun moves lower in the western sky. So, some shade will reduce heat stress during the hot months. Happy planting!

Madlyn88, not much you can do. Tree roots, as is true of above ground parts, do not "heal" but are able to wall off wounds and grow around them. For the most part, nothing we apply aids this process. This is most likely what will happen here. Provided the tree is otherwise healthy and vigorous enough, it will take care of itself. +oM