Nothing new to comment on in most of the logic blogs I've been following, so I'm going to reference the Stanford Encyclopedia of Philosophy article on Many-valued logic.
I may also from time to time discuss other articles.
As I've already noted, the prevailing opinion among logicians is that the development of modal logic on the basis of 3-valued logic never succeeded, but I cannot find where the attempt is documented. I've examined the standard literature on many-valued logic, including the works Ackermann, Bolc and Borowitz, Malinowski, Rescher, and Rosser and Turquettee, and none of them discuss it in any detail. I've also checked the references on modal logic, e.g. Hughes and Cresswell, and they don't discuss it either. There is a proof that the Lewis systems can't be reduced to three values, but then my system isn't exactly one of them, so the conditions of the proof don't apply.
There is some connection between the strict conditional I use and the issues related to relevance logic. Some of the paradoxes of material and strict implication can be addressed.
There is also a connection with paraconsistent logic and issues related to that subject.