Other than the buzzword "timeless physics", this doesn't go beyond anything that I knew about in 1991 (when I was older than Harry but still in high school and had never heard of Julian Barbour). This is implicit in Minkowski's formulation of special relativity (1908) and Heisenberg's formulation of quantum mechanics (1925); I don't know who made it explicit, but I probably read about it in popular science books.

ETA: The buzzword that I knew then (or perhaps learnt later and immediately connected to what I knew then, I'm no longer sure) is "block universe".