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This. Aim to cut perpendicular to the branch so you end up with a circular cut instead of a big oval. Do an undercut first so that the bark doesn’t tear down the trunk and cause a wound. The lower the cut is down the trunk and the larger the diameter the higher the risk though. I’d be inclined to make a couple of cuts further up instead of losing the whole limb but that’s just the hippie-arborist in me talking.
Maggies are tough as nails and can handle losing a limb or two so should be fine.
It looks like it could do with a light thinning through the middle of the lower crown as well. Send the kids up with a pair or secateurs :)
Trees are tough mofos, which anyone who's tried to kill one will confirm, so I'd just lop the fucker off. Angle the cut in such a way that any water will run off, as that's one way it can cause more widespread damage to the tree.