By one-off, you mean do it once and never again? Sorry, no such thing. You can by various chemical or organic means get rid of all the aphids on your tree. You can't get rid of all the aphids in the world, so eventually they will come back.
Not sure what the neighbors are complaining about. If it is your tree, why do they care if it has lots of aphids? Not like your tree is the only source of aphids to come in to their yard.
I agree with applestar. There are always going to be aphids. When there is a major infestation of aphids, enough to significantly damage a tree, it is because things are out of balance. When the system is in balance, there are aphids and there are ladybugs and lacewings and praying mantis and grasshoppers and hoverfly larvae and chickadees and titmice and warblers and frogs and toads. All those other things eat aphids. If there are enough of the other things, there will always be some aphids, but there will never be major infestation.
While you are working to create a system that is in balance, with habitat to attract some of all those other things, some of them like ladybugs and praying mantis can be imported in to your yard, you can buy them on line.