While I agree with @cybmeta that it sounds like an edge case considering WP, it's a reasonable requirement. And we throw out questions that are too general :-)
I'm sidestepping your exact question a little, as I can see that creating a number of posts and forcing their slugs to be non-unique might be a recipe for future disaster. What do you do to the slugs if you have a House 2 in Project A, a House 2 in Project B and someone changes them both to be in Project B? And House 3 on Project B is never ever really going to need to move to Project D, is it? I've a feeling that a taxonomy isn't the right thing here.
If this was my coding project, I'd define two CPTs for
houses, building customisations into the WP admin screens to allow me to assign
houses as child posts of
projects. A bit like
Posts/Pages & their attached
Attachments. (I've done something similar in the past for Product Variations/Options but never got the interface right due to lack of time/budget on the job.)