Can "believed" ever be an adjective?

From the four criteria considered to be the common characteristics of adjectives (CGEL § 7.2 p. 402), can be concluded that "believed" tends towards the status of a full adjective but that its use is subject to much idiomatic constraint.

A) attributive function: Yes but rarely unmodified and if so noun sensitive¹
B) predicative function: Yes but idiomatically restricted
C) modification by very: No
D) comparative and superlative form: Yes but idiomatically restricted

"Believed X" used if X is one of the following: story, tale, principle, notion.

(generally believed fact)

A (2014 - believed proposition) Our paradigm for such basing is the case in which we make a conscious inference from one or more believed propositions to another one.

D (2012) In the relative sense, then, the sense in which we contrast reality with simple unreality, and in which one thing is said to have more reality than another, and to be more believed, reality means simply relation to our emotional and active life.

B (2012) . were more familiar and more believed than any of the identified folk beliefs.

D (2010) as to render the metal of our true English valour to be the more believed and feared abroad,

B D (1760) But his dying so “ critically , as it were in the minute in which he seemed " to begin a turn of affairs , made it to be generally the “ more believed , and that the papists had done it , either " by the means of some of lady Portsmouth's servants , or ...

D (2012) In the relative sense, then, the sense in which we contrast reality with simple unreality, and in which one thing is said to have more reality than another, and to be more believed, reality means simply relation to our emotional and active life.

B D (2014) A speaker who can look a person in the eyes when speaking with them is more believed and trusted.

B D (1820) .. and the state or necessity “ of Bishops be more believed.

B D (2010) The more specific the praise is, the more believed and appreciated it will be.

A (2008) I do believe there are more believed lies told in June than any other month—

This reference shows that "very believed" is considered to be incorrect: 1981 - Lexical Rules of Semantic Interpretation: Control and NP Movement in English and Polish.

¹_{Observation due to user Edwin Ashworth}