This is a new idea to me. I like it a lot.

One way to make it eventually explain the Born probabilities is to also throw away continuity of experience and instead use something like ASSA: "your current observer-moment is a random sample from all observer-moments", where the "measure" of each observer-moment is determined by its description complexity as you suggest. Then you could look at the universal wavefunction (without postulating the Born probabilities) and note that pointing out a human observer-moment after a split has occurred requires 1 bit more information than pointing out the version before the split. I have no idea if it's true, but it sounds quite plausible to me.