Yeah ..just to reiterate though, if there is any doubt that services (gas, electric, cable TV etc) may be near by get somebody qualified to double-check before you allow anyone to dig.
is it possible to just cut back (?chop down) the field maple to remove it? Moving it/ taking out the root etc sounds like it could be rather disruptive.
I get the impression they self seed quite easily, so it doesn't seem like such a loss in a way, if it needs to go from by that wall.
Cut it down, then carefully paint the end with stump/brushwood killer. Cover the stump with a plastic bag firmly tied on to protect children, dogs, cats & wildlife etc. It won't regrow and can be removed when it has rooted sufficiently.
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Moving it/ taking out the root etc sounds like it could be rather disruptive.
I get the impression they self seed quite easily, so it doesn't seem like such a loss in a way, if it needs to go from by that wall.