Use of "Proper" as a postpositive adjective

I have an inkling that the following word usage is grammatically-correct; however, it is immensely difficult to search for confirmation, as all I receive for queries like "Proper as an adjective" are reams of results on "Proper adjectives". The word itself I am using as a postpositive adjective, similar in form to the phrase "time immemorial".

The shelter remains in name only; the shelter proper is in another town.

Work in theory remained, although operations proper had mostly been outsourced.

Can anyone advise?

Perfectly grammatical.

The OED, s.v. proper, a., definition 7.c, says:

c. Strictly or accurately so called; in the strict use of the word; genuine, real. In later use freq. as postmodifier.

The earliest example of this use that it quotes is 1807: "The earths proper do not unite with oxygen... Characters of the alkaline and proper earths."