Our neighbour has moved 3 quite large trees from woodland. He did it quite roughly but one has survived beautifully, a second is a half success but the third didn't take. He didn't try watering them in even.
I know that you can move fairly large trees - there is quite an international trade in hauling out large trees to send abroad for Chelsea and so on.
I think it's well worth a go, even with a hedge. Coppice it right back to about 6" above the ground, dig out along each side then take out the plants. I'm not sure if you need to keep a large ball of soil around the roots, or just do them like bare rooted. I think there will be a lot of root damage, but by coppicing them first they have the best chance of survival, and they will not rock in the wind. Have the holes open for planting them into so the roots have no chance to dry out, then water them in thoroughly (or do it before it rains heavily)
For trees such as the oak, I'm sure they can be moved without coppicing, but stake them very securely in their new positions.
I have no experience of doing this, so it's just a suggestion