A Chinookan etymology for ‘mirror’

Looking Glass Creek, chinook salmon habitat (image credit: CRITFC)
A super-charming Clackamas Upper Chinookan recollection tells of the people using the first frying pans they were given as mirrors…
Here is a great passage from it, in English and in Clackamas:
In the first line, the word
ančx̣ilúkšdima ‘we used (them) for looking’ sure seems related to an early Chinuk Wawa word for ‘mirror’, known as early as Demers-Blanchet-St Onge’s 1871 [1838-early 1840s data] < shilakom > / < shilakompe > ‘looking-glass’, and still found in dictionaries made from 1860s data.
Some Jargon word lists represent this noun clearly with a “CH” rather than a “SH” sound, matching up with at least the č (and probably with the sequence čx̣) in the Chinookan word above. (A correspondence with čx̣ is perfectly probable; compare how virtually all old dictionaries wrote chxi ‘new’ as < chee >.)
My project of learning Chinookan-language grammar is ongoing, so I don’t yet have an analysis of the literal meaning of < shilakom > / < shilakompe >. But I can find the root in the word, -kšt / -kst ‘to look’ (as opposed to -kəl ‘to see’). Maybe it contains -x̣ Reflexive. Maybe the < -pe > at the end of the longer variant is the Locative suffix -pa. Maybe the literal meaning in Chinookan is roughly ‘you look at yourself in it’.
Fun bonus fact:
Also in early contact years, there appears to have been a Lower Chehalis Salish word for ‘mirror’ that meant literally ‘device for looking at oneself’. It got loaned into neighboring Salish languages (incuding in ‘spectacles’, literally ‘eye-mirrors’!). That pattern recurred with a number of newly introduced items. In other words, not only Chinuk Wawa but also one of the tribal languages of the “Chinooks” supplied a chunk of vocabulary for new trade items way back in the day!
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