Does Dogen's wholehearted way say anything about the status of memory?
If you are referring to the intellectual capability of memory (隨念智), then this is not mentioned in Bendowa.

The whole-hearted way is, as you say, awareness from moment to moment. According to Zen, it is the experiential reality, not the memory or interpretation thereof (even if the memory is one of realization). The memory of a previous realization cannot help you. It will in fact hinder you if it arises. This is well explained in Mumonkan case 22:

Ananda asked Kashyapa, "The World-honored One gave you the golden robe; did he give you anything else.
"Ananda!" cried Kashyapa.
"Yes, sir!" answered Ananda.
"Knock down the flagpole at the gate," said Kashyapa.