I have been studying and collecting the 1922 Series Springfields for more than 30 years.
The first 2,200 or so were stamped Model of 1922. Serials were from 1 through approx 2200.
The second model was the 1922M1 and marked as such on the receiver ring. Serial numbers of these started over with 1 and went to 20200 or so. Many of these had the bolt, stock, and magazine upgraded with with the M2 parts and the Model number on the receiver ring had an additional 1 stamped after the 1922M1 making it read 1922M11. When this was done, starting in about 1935 a B was stamped after the serial number.
The M2 rifles started again with serial number 1 and went above 20000.
Some 1903 receivers were converted from .30 cal to .22 LR by Sedgley. I have one that was converted to .22 WRF. I have seen many that were converted to .22 by installing an M2 Bolt and M2 barrel . Most of these remain as single shot.
Unfortunately you have a modified .30 Cal.
This is a brief explanation of the 1922 Series I know of no book that has been written expressley about the Springfield .22s. They are mentioned in periodical magazines and
books written about the 1903s.