The first reference I have for the "Ported air sleeve" is in the 1912 to 1918 parts book and it is listed as follows:
DA 2000 Ported air sleeve ( for fast motors ) 1914-1916
FA 2006 Ported air sleeve ( for fast motors ) 1917 and 1918
My next parts book is published for release August 1st 1922 and covers 1917 to 1923 models
FA 2006 Ported air sleeve ( for fast motors ) 1917 to 1923 61 cu in
DA 2006 Ported air sleeve 1921 to 1923 74 cu in
Then in the parts book published for release August 1st 1923 (one year later) and covering 1920 to 1924 models the ported air sleeve has been dropped.
I have examples of FA 2006 and DA2006 and the only difference is that FA2006 is designed for the 1 1/8 bore 160 series carbs and DA 2006 is designed for the 1 3/8 bore 180 series carbs but exactly what DA 2000 looks like or what model it was intended for I don't know.
From the parts book and the fact that your one is fitted to a HX 181 carb my guess would be that it came off a 1921 to 1923 74 cu inch JD Harley.
My research suggests that although these air sleeves were commonly used in racing applications in the quest for more power they were initially used on road applications to try and solve some of the high speed carb problems that occured with Model H carbs.
If you ever do flow tests on the air valve or as we call it the flutter valve assembly you will see what I mean and the engineers of the time must have realised this and developed the ported air sleeve in an effort to allow the engines to breath in more air at higher speeds.
Because there is so little Schebler info out there, there is no positive date for the introduction of the Deluxe carb but once again my guess would be that it's introduction wolud see the demise of the ported air sleeve and maybe that date is in the 1922-23 period we are discussing.
Hope this helps.
Peter Thomson, a.k.a. Tommo
A.M.C.A. # 2777
Palmerston North, New Zealand.