Well Doug I think I would use the backhoe in this situation. I believe I would trim enough branches to get the bucket behind the shrubs the best I could and cut as many shallow roots as possible. To me the chain and pull method would cause tire spin and do a real number on the grass. Instead I would hook a chain to the backhoe and try to pull with the hydraulics from as high up as the trunk is rigid. You should be able to watch the ground and see how much force is being exerted on the foundation side. My thinking is that footings are pretty deep in your area so the odds of major roots growing under them are slim.
Now if the utility marker shows any utilities running under the shrubs it would start looking like a ‘do it by hand’ type of job and I’d walk away. You could also cut a branch and take it to a local nursery and they should be able to identify the shrub and have an idea of what its root structure is like.
Good luck,
MarkV