That is, I can value preserving the continuity of my memory in the short term, even while acknowledging that in the long term all the bits that are currently in my memory will be more-or-less lost even if "I survive indefinitely" (in square quotes because I don't believe that "I" means something coherent in the context of indefinite survival, which makes the phrase intrinsically misleading).

Well, there's no obvious incoherence in caring about the ancestral of memory-connectedness instead of, or in addition to, connectedness itself. (Parfit talks about this in Reasons and Persons.) You could even define "yourself" via the ancestral, in which case "you" could indeed survive indefinitely, provided that in each year you have strong memories of the previous year.

Not that I find this idea particularly attractive. Instead, looking in a cold clear light at what I care about when it comes to survival, there are two strands. One is as XiXiDu mentions: I want (an) agent(s) to continue pursuit of my goals. But the deeper emotional attraction comes from anticipating good experiences. And the identity constraint on anticipating good experiences is: absolutely none. I can anticipate your good future just as sensibly as I can anticipate mine, provided that I can understand what would be a good experience for you - or for that matter, provided I can understand what would be a good experience for my future self.