I took a look at Julian Barbour's "time capsules" and his Nows may be like my kernels but in my (2) the sequence of kernels is inconsistent with its past due to the "=>>" dynamic as I have indicated.
Barbour's idea is that there is no sequence to the time capsules at all, they all exist independently in a timeless manner. Some time capsules may contain records that appear more or less consistent with other time capsules, and the number of other capsules which have records consistent with a given capsule may have something to do with determining the probability of that time capsule, but there is no objective truth about the future or past of a given time capsule. Here's a good discussion of his theory, I don't know if you already read this one or not:
He also wrote a book explaining his idea at greater length, called "The End of Time":