Just how did Redgrave arrive at their first conclusion

1866 Richard (1804-1888) and Samuel (1802-1876) (writing 'A Century of Painters') examine the catalogues and conclude that Turner's first exhibited oil is 'Moonlight'.

Turner's first four exhibited oils were

1793 An oil in the Anti-Room

1796 Fishermen At Sea [TATE Size: 36" x 48"] in the Anti-Room

1797 Moonlight, A Study At Millbank [TATE panel, Size: 12" x 16"] in the Great Room

1797 Fishermen Coming A Shore At Sun Set, Previous To A Gale [LOST (Mildmay) Size: 36" x 48"] (In the list of exhibitors Turner's picture was at 279 (in the Great Room) but it was swapped with a picture by Sir F Bourgeois RA because the latter did not want his picture in the Anti-Room.) another Turner oil was hung in the Great Room, No.279, 'Fishermen Coming A Shore At Sun Set, Previous To A Gale' and later moved to the Anti-Room following a dispute between the hanging committee and Sir Francis Bourgeois RA. This action alone would have indicated to the Redgrave Brothers that oils were hung in the Anti-Room.

Redgraves worked from the RA Catalogues - they said this (in relation to another artist)

Or perhaps they thought that Moonlight was the Bell picture painted before Rising Squall

...already alluded to

Page 84 source Mr Warnum - possibly R. W. Warnum fl.c.1849
Anecdotes of Painting in England (edited by RW Warnum) vol i, 1849

Page 85 source Peter Cunningham

Munro page 84