Read the Ca'Non sentence from the "Smithsonian Go Figure app":

{tera jar Soch, DIS wa Hut jav

Hut, maSDaq SaqmeH Qu' wa'DIch

HochHom turlu'taHvIS, wej logh

lengwIpu pa'mey 'oH Apollo wamaH wa' ra'ghom bobcho Columbia'e'}

"Apollo 11 Command Module, Columbia, was the living quarters for the three-person crew during most of the first manned lunar landing mission in July 1969".

The {Qu' wa'DIch} is obviously the subject of {SaqmeH}. It can't be the {Qu' wa'DIch HochHom} since the goal wasn't for "almost all of the mission to land on the moon".

And then we have the {HochHom turlu'taHvIS} which is used to express the "during most of the first manned lunar landing mission".

However, since the subject of the {SaqmeH} is only the {Qu' wa'DIch}, shouldn't there be a comma right after it ?

maSDaq SaqmeH Qu' wa'DIch HochHom turlu'taHvIS
while most of the first moon-landing mission was being carried out

This is a single while clause.

X turlu'taHvIS
while one does X

The X is a noun phrase, maSDaq SaqmeH Qu' wa'DIch HochHom most of the first mission-to-land-on-the-moon.

A SaqmeH Qu' is a landing mission, a mission for landing. Remember that purposes clauses can be attached to nouns that are not the subject of that clause. Qu' is not the subject of SaqmeH.

If that mission happens at the moon, it is a maSDaq SaqmeH Qu' landing mission on the moon. The locative is added to the verb as usual. The fact that this verb is part of a dependent clause is irrelevant.

It's the first moon-landing mission, maSDaq SaqmeH Qu' wa'DIch.

We're only talking about most of the mission: maSDaq SaqmeH Qu' wa'DIch HochHom.

-- 
SuStel
http://trimboli.name