The Age and thickness of this tree could be a problem. Trees and other plants grow by a process called geotropism which means they grow towards the sun and are also affected by gravety. If the shoots are growing down and parralell the problem is the tree is too thick and it has no sunlight to grow towards. The branches that are growing out are trying to find the sunlight and the ones growing down are being pulled there by gravety. I would thin the tree out in the fall to Early Spring to filter sunlight through there and see if that works. This would be my guess knowing the age of the tree and knowing most bradford owners this tree is not well maintained.