Might have found the elusive 1920's manual, but it's not 1920's. It might first have been 1920's. It is still out of print, but apparently was reprinted as late as 1979. Same name (almost) and reads as if it might be the manual in question "U.S. Cavalry Manual of Horse Management" is the manual in question and this is "Cavalry Manual of Horse Management". Still came out of Ft. Riley and used during the time between WWI and WWII, so it might be the same. 1920 was shortly after WWI.
You can get a general look at it. Check this link and see what you think. Cavalry Manual Of Horse Management By Editor-Frederick L. Devereux - Used Books - Hardcover - 1979 - from Gadzooks Books and Biblio.com
I have to agree that you don't need a special saddle and that you need to free up the shoulders on a gaited horse. I have a gaited Stubben saddle that is for sale and it is extremely comfortable for both rider and horse. The only reason I am selling it is I have too many saddles. It is in mint condition. It gives the horse lots of leg contact and it perfect for trail riding. I could send you a picture by email if you would like to see it.