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 projects
and 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.)