Taking θεὸς as a predicate is unjustifiable where it is preceded by an article. There is no grammar rule which allows an adjective/participle in the first attributive position to be disassociated from its head noun by a supervening rule of construction.Despite the fact that we are working with an attributive participle, the participle still retains an equative function just like its finite counterparts. There is no "disassociating it," because we take θεὸς as a predicate.
The first attributive position takes precedence over apposition and any attempt to divide the participle clause, where ὢν doesn't immediately follow it's alleged head noun.
To say that ὢν is equative to an antecedent noun is tautological, as predicting an outcome, rather than justifying it. ὢν isn't equative to an antecedent noun in John 3:31, and doesn't always function equatively, which is a semantic observation, not a grammatical proposition.
I agree that in Rev 19:21, the participle phrase operates adjectivally at the semantic level, and there is no doubt that it does because τῇ ἐκπορευομένῃ is dependent and follows its referent. It is a case of both apposition and the semantics of the phrase coming together to enable an adjectival rendering.I'm not following you here. There is one usage of a substantival participle in the head noun phrase (τοῦ καθημένου, "of him who sat"), and an attributive participle that sets off a participial phrase that operates adjectivally (τῇ ἐκπορευομένῃ, "which proceeded"). Is that what you are referring to?
But within its own dependent clause τῇ (ἐξελθούσῃ) has a substantival character and is gramatically appositively because it isn't relatable to what immediately precedes it.
A literal English transcription would like to see a comma after the rendering of τοῦ καθημένου ἐπὶ τοῦ ἵππου, with τῇ being transcribed as "it," for the English rendering: "with the sword of him that sat upon the horse having proceeded out of his mouth" lacks clarity and style, although it remains plausible but only due to the unambiguous meaning.
Hypothetically, were τῇ ἐξελθούσῃ ἐκ τοῦ στόματος αὐτοῦ to have been followed by a noun in the dative, and / or a suitable verb, it could have been made into an object clause within a subsequent sentence.
That is to say, the semantic rendering of a hypothetically appositive participle clause, and especially of what appears to be a complete subsequent sentence in which a participle occurs, is not independent of the natural gramatical construction of that clause/sentence.