IMHO S na and Q as are not interchangeable in this sense. Na is more instrumental (and also loaded with other senses which only confuses the context  - pun intended); as is comitative.
"Text" does not necessarily need to imply written text IMHO, so it could equally come from nyar, pahta, quet, carpa, tec.

Also I assume the cognate of Q sarme would be something like *sarf; also, na- would cause a lenition.

I actually tried to use the S word nan, wich causes nasal mutation, thus nasarf (with your correction). The S cognate of Q nyar- seems to be nara-. Maybe then nanarad, but that's impossible to tell apart from na + narad.

If you want to use the preposition combined with the article as a prefix I suggest you attach it with a hyphen, to make things clearer.
The question to me is, do we have to create a calque on context or could we come up with an alternative to that etymology.

No, the general meaning would work just fine I suppose.

*golain/*pele/*ostanneth/*osgae(–f, –n) en-nad ? (The second element in the fourth neoword is from KAY-.)

+ܤܡܝ ܦܠܕܢܝܘܤ  with thread?/no idea/around signs?/around lie?/of the thing?

*Go-lain (cp. German Zusammenhang & Latin textus) is intended to connote a collective sense [i.e. "threadage"] in the manner of gochel, golas, gwaloth.

*Pele is from PEL-ES < PEL (cp. TEL-ES, Etym:391-2). The attested word ephel had the definition "surrounding ring" in PE17:87, btw.

*Ostanneth [vs. *othor < OS *os-re/ro] is a prestanneth –type noun based on the Goldogrin-stage verb osta- "to surround (build up, fortify, protect)".

Here nad is of course expected to govern the full sense "thing, affair, matter" (like Goldogrin nath, cith did).

I was thinking along the same lines - to take AR, PEL, or YOD and create a noun with the generic meaning of "surroundings, milieu, environs, neighborhood", and use that by extension for "context".

*catamen "background" from ca/cata/cana and men

Maybe golain for more of "connection, context, realation" and one of the other, say osgaef for more of "surroundings, milieu".

catamen as a Q word?

+Hjalmar Holm yes