Meaning of S4/BLCE/1/7Edit
A little bit of Wikipedia searching turned up the phrase Logistics Combat Element (LCE) - basically, in the US Marine Corps any Air-Ground Combat Task Force (a Marine Expeditionary Force, Marine Expeditionary Brigade or Marine Expeditionary Unit, basically the various-sized building blocks of the USMC at large) is based around a Command Element (CE), a Ground Combat Element (GCE), an Aviation Combat Element (ACE) and Logistics Combat Element (LCE). As for the B, well, we'll start at the top. Structurally, a Marine Expeditionary Force is based around a Marine Division (the GCE) and a Logistics Group (a division-equivalent LCE), with an Air Wing as the ACE and an Information Group as the CE. That's probably a little too large scale to give us any clues.
But a Marine Expeditionary Brigade has a Regimental Combat Team (a regiment) and a Combat Logistics Regiment (or CLR). The possibility exists that the UNSC's version of that would be a Brigade Logistics Combat Element. But, in addition to diverging from the fact that USMC Brigade LCE's are specified as that regiments (though some divergence is obviously fair), it also kinda messes with the 1/7. We know from Palace Hotel that a similar unit, E2-BAG/1/7 (referred to as 1/7/E2-BAG in the story but altered on the OG B-net UNSC weapons pages for Halo 3 which include quotes from members of the unit), the 1/7 likely means 1st Battalion, 7th Marines (as First Platoon, Kilo Company is specified beneath it).
So let's go one deeper, to what would be the UNSC's equivalent of Marine Expeditionary Unit, which is based around a battalion, an aircraft element, and a Combat Logistics Battalion (or CLB). Once again, we could be looking at Battalion Logistics Combat Element for BLCE. Now, departing somewhat from what we see today, that could be a battalion in and of itself (which means it'd probably be more "Battalion, Logistics Combat Element") or the LCE's of the UNSC Marine Corps' version of an Air-Ground Combat Task Force (AGCTF) are not considered to be battalions or regiments but are actually part of the battalion to which it is attached. The Logistics Combat Element of the 1st Battalion, 7th Marines.
As for the S4, the working assumption is that translates to Sol IV, as in Mars (since the E2 in E2-BAG/1/7 supposedly translates to Eridanus II). So, going off the extrapolations we've made so far, what we've got is S4/BLCE/1/7 Battalion Logistics Combat Element, 1st Battalion, 7th Marines, out of Mars. I suppose the implication of such a setup would be that MEU-level UNSC Marine Corps unit is thought of more as a single battalion reinforced with supporting elements that are considered part of the battalion, rather than multiple battalion-equivalent units of different function working together.
That alteration could be a result of the UNSC's unusually high "tooth-to-tail" ratio that we read about in the Spartan Field Manual, which means a high ratio of combat troops to support troops. In this case, the support element may not actually be large enough to be considered its own battalion, and so is folded into the battalion it's attached to.
Just to clear up any confusion that may have risen relating to the 1/7 thing, though, I'm personally operating off the assumption that E2-BAG/1/7 and S4/BLCE/1/7 are part of different battalions, from different regiments. The alternative is that you've got a single battalion with a BAG (Battalion Assault Group, potentially, perhaps referring to some portion of the battalion's fighting troops, maybe heavier armed ones) from an Outer Colony world (Eridanus 2), and a BLCE from a Sol colony (Mars). Not necessarily inconceivable, but highly unlikely. Presumably (if both truly are to be considered canon and not instances of 7 being used as a placeholder) that means there's some overlap in Regimental numbering, differentiated by homeworld - that there's a 7th Eridanus II Regiment, and a 7th Martian Regiment, both of which fought on Earth in 2552.
Just jotting these thoughts down here in case additional information becomes available in the future.
Relevant links: https://en.wikipedia.org/wiki/Logistics_combat_element https://en.wikipedia.org/wiki/Marine_Air-Ground_Task_Force --Grim Looters (talk) 20:15, October 23, 2019 (EDT)