Here’s my stream of consciousness as I ran down your story. None of this is meant to be critical of your work.
Your first cite is obsolete. Ref the official source DODD 1005.8 is not current. The pdf you cite from wherever you got it is certified current 17 years ago. A search for directives containing the word “precedence” also comes up empty.
Your second cite looks pretty good. Although the DOD Order is not about precedence of the services. It’s about seating & social precedence of people in various jobs in the services. Though yes, as a general matter it says a USMC official comes before his/her equivalent at USN. Though the Order gives no rationale for this sequence.
Your third cite from the Department of Agriculture talking about flag display at Exchanges is really odd. Why is DOA opining on this in the first place? They cite 1005.8 which we know (at least as of 2003) does not say anything about flags and as of 2020 does not exist at all.
Given that’s all wrong, I would not put much weight on DOA’s unsupported assertion that age of the service is the determinant of precedence. As well, the Coast Guard predates the USAF by a good 150 years but is precedentially after it. So clearly age is not the discriminant. It might be a tie breaker, but we don’t have ties. IMO somebody out there in DOA land is confused.
The fourth cite to wiki on the Anthem memorial asserts the precedence but has no cite for where that came form. All of the wiki article’s cites simply say “DOD precedence” in the same wording; presumably all copied from one another.
The fifth cite on wiki simply makes the same tired assertion again in the opening paragraph. But now we’re finally getting somewhere. …
Cite #2 of that wiki article is to a Wayback Machine page. The original page that WayBack captured is now gone to the great webpage graveyard in CyberSpace, but it appears the page was written some time around 2008. The article cites our old friend 1005.8 which apparently existed in some form then. And proceeds to give us a decent explanation, while admitting there are some loose ends and conflicting theories out there.
The short version is that per this historian’s favorite theory the process of spinning up each service was not instantaneous and USMC managed to be legally formed later, but functionally operational earlier. In fact operationally it was the earliest of the services, despite coming second in precedence to the Army.
That was fun.
Also from this I learned something else cool and totally unexpected. Back in 2017 DoD extended online Exchange privileges to honorably discharged veterans. WHich is me. Not having, retired, not being disabled, and not being broke or homeless, I’ve come to accept that my service has zero benefits after my separation back in the 1980s. Not so. I too can use the Bx online. Cool! Now to see if they have anything interesting that Target doesn’t.