Your vet is quite right - surgical removal of his tail now would be a full amputation. No different from removing a limb.
The reason docking is done within the first 3 days of life is that it is thought that the nerves are not fully developed at that point, and cutting the tail off won't significantly impact the dog (in the long term).
This does NOT hold true beyond those first few days of life. His nerves are most certainly properly developed and it would be both a major surgery (the tail is an extension of the spine - so you're not talking about some minor bit of the dog here) and a very painful one, with a significant recovery time. Ask any human amputee and you'll find that it rarely ends there - many report ongoing problems, including 'phantom pain' in the non-existent body part for the rest of their lives.
I do not think it is reasonable to consider an amputation without a strong medical reason for it (that is, an irreparable injury). Unscheduled coffee table clearances via tails don't count
Young boxers take time to learn to calm down, especially when people arrive home. You can help by ignoring him when you first get in - for a good 10 minutes or more, until after he's calmed down. If you give him attention, you increase his excitement. On the other hand, if he never even gets greeted until he's calm, he'll learn to calm down faster. It won't change things in 5 minutes, but over time almost certainly will.