Greg,
I found this in the Archives:
https://www.eisenhower.archives.gov/research/finding_aids/pdf/US_Army_Unit_Records_Index.pdf
It's a listing of all the army units in service between WI and WWII. Both the 29th Infantry and the 29th Engineers and a Company E.
Years ago, I was looking for information about my grandfather's military service records. They were destroyed in the fire at the repository in St. Louis in 1973. I wrote to the US Army Military History Institute, Carlisle Barracks, Building 22, Carlisle, PA 17013-5008. They were able to give me information on both my grandfathers--the training camps they went to, where my maternal grandfather served overseas, where he suffered a gas attack in France, all sorts of information. You might try contacting them to see if they have more information.
There were conflicting serial numbers on CWB's military records; on his request for interment it was R-317616, and on his WWII draft card the serial number was U-2914. I believe the first to be correct, based on the number of digits in other servicemen's records I have looked up.