Man that is such a cool find. I feel you on the frustration of trying to match old work though, because you just can't fake that raked look with modern tools and mortar mix. I ran into something similar on a place from the 1820s and ended up trying to match it with a homemade jointer stuck in a piece of wood. It took forever and honestly it still wasn't quite right, but the owner appreciated the effort. Part of me says just lay a normal joint and move on, but the other part hates covering up something that's been sitting there for two centuries. It's a tough call and I don't envy you having to make it.

The separate line item is the key part, once it touches their books as its own invoice it stops being a suggestion. Only backfire I had was a client who just ghosted instead of paying, but honestly I'd rather lose that one than chase them for free.