John, Grand idea!!
I'm not sure which one the # 55 is but I have the one Dave put out which he dates as 1940 -42 and it has the selection of burners which are basically " round" and "star", 3 styles of each with the series of stove pn's that each will fit.
Well, you made me really go look. Catalog 45 reprinted by Larry and Sue Foxx, which has a note on it that nearly all of the items in it were discontinued prior to 1915, lists just 3 burners. They are described as " drilled cap", " sawed cap" and " the tangent arm one-piece drilled burner" .
Then we have Catalog 47, printed by LW Book Sales, circa 1918 which has 4 pages of burners primarily all either " drilled" or " sawed". No stars.
So it seems the round drilled burner was around long before the star burner which, according to the books I have, must have shown up sometime between 1918 and 1940.
And thanks for your question as it really screwed up my coffee time this morning. LOL