Theory popped up on my third listen.
After the episode opens Saul says:

Some old lifer once told me that after a few months you start to forget things…but after five…it’s been a long time since I wrote much of anything down. The tower fell around the beginning of August and now it’s December….now I’m playing a little catch up writing in this. I guess there wasn’t any good reason until now. But I’m gonna back up a little to November 27th.
The soldiers report it to be December 1st.

What is UNTIL NOW? By the date given this could be as little four dates after November 27th, to 34 days. [December 1st, to December 31] Maybe he is reporting the incident to someone…maybe Fort Irwin? He got the patch from the body, so he would know that he came from Fort Irwin [it could be a fake to Saul but he’s a shoot first kind of person], the tape nametag would indicate that he is newer because in this instance they can’t get a nametape as fast as they would before.