Leave all the normal headstone stuff on the headstone. Also add a QR code, like these mortuaries are doing. But instead of making it just a URL to some sort of memorial page for the deceased, encode their obituary into the plaintext of the QR directly, and add a URL to the memorial page at the end of that text for people who want to see photos or sign a digital guestbook or whatever. That means that, even if the mortuary goes out of business and the URL no longer leads anywhere, the obituary is still readable by anyone with a smartphone.

That's my guess.