Don't. Having an over hang would just look odd. Along with the thing that in some areas the toilet must be a certain distance from any other object. Which is a problem I have with redoing my current bathroom if I want to bring it to current city requirements.

That sounds like a bad idea. It would look like a mistake and make me wonder what other mistakes you made on any work you did on he house.

Tell him to stick with RE and stay out of design.

Nope. It will look weird and you will bump your shoulder when you use the toilet. The overhang will be unstable. If you need to replace the counter, do it. But don't add six inches in such a cramped space. From a listing standpoint, removing clutter, and fresh, neutral paint will create an illusion of more space.

Can you share a picture of your bathroom? Is the vanity 22" or 24"? Can you replace the sink for a smaller one? If installing a 30" vanity is still to code (with the toilet beside it), I would do it.