Exactly, there is no need for any third party. Alice implements the spending rules and then shares 2 params <Alice Public Key> and <N days> with Bob along with the signed (but not broadcasted yet) tx from A to E.
So when the tx is broadcasted to E each of the parties can spend from E by reconstructing spending script from the params.

Normally this is Bob (a heir) who will broadcast the tx and spend from E when inheritance time comes.

P.S. As I figured it out recently answering posts in this topic, the process can be even more simplified with elimination for the escrow (E) address  And some parts of this approach still can be used. I'll share more details later as I need to put some effort for simple explanation.