Should "harmonized what science tells us" be "harmonized with what science tells us"?

Yes.

I would have said 'reconciled' instead of harmonized, but yes.

"Very well, so the six days of creation can be harmonized what science tells us about the natural world."

I suppose the answer would be if the writer wanted to harmonize creation with science or harmonize creation with the natural world.

Missing 'with'

... the six days of creation can be harmonized with what science tells us about the natural world.