It will be interesting to see what your find!
I believe if you test all 960 starting positions, with all first moves for white (20), and all first moves for black (20) you will have 960 x 20 x 20 = 384,000 openings to test. (maybe a few less when the knights don't have two places for their first move).
So I think your way is better.
I'm planning to post here evaluations of all 960 initial positions (in lexicographic order) using the local analysis board (Stockfish at d=30+). At the moment, only the first best move is indicated.
BBNNQRKR [+0.3] 1.d4 f5 pseudo-Dutch
BBNNRKQR [+0.7] 1.f3 h5 pseudo-Barnes
--- to be continued ---