In the past I've noted that the Kin list is the one thing a character completely loses upon dieing, when you inherit you can get back some portion of your LP even at full change, and all your physical resources on a claim, but that Kin list is just GONZO and if your say a trader or someone doing a lot of communicating your royally screwed. I've said it should be inheritable but an alternative solution is to simply allow us to write kin lists as physical game objects so they can be inherited along with other items.
This kin list on parchment would be called a 'Family Tree' and requires a parchment/ink/quil and naturally Ancestor Worship to make, in the interface option to make it you have a 'write' button corresponding to each kin color so you can make a sub-set of what ever portion/s of your kin list you want. The list is recorded with hidden hearth secrets, the player/client never sees the hearth secrets or even the names on the it but the Family Tree object gives you a way to pseudo-anonymously kin them by hearth secret. If someone on the Family Tree changes hearth secrets after the Family Tree is made the link is broken and that person is effectively not on the Family Tree anymore. When someone has the Tree they can do a mass 'Kin all' from it. This will be excellent for both inheritor but also to rapidly get a new member kinned to a large group, just hand them the Family Tree and they can Kin the whole group in one go rather then having to laboriously propagate HS to everyone. It also means HS are kept more secure because they stay more secret and the chance for people to try to spawn of them for grief/spy purposes are greatly reduced.