(i) Ex (5) and (7) show no hag, indicating the correctness of a relative rather than a coordinate analysis, unlike for English Sir Pitt has been and proposed for to marry Miss Sharp (= Sir Pitt proposed to marry Miss Sharp, plus surprise) (Oxford English Dictionary, s.v. be). Interestingly, no example with ma occurs, which alternates with e, hag e in the case of overt temporal heads.
(ii) Gourmelon gives dialectal indications for his ex, these should be kept, because it allows comparing rannigs and usage of hag with overt temporal heads (e.g. in Urien's investigation of these matters for Leon).
(iii) Gourmelon's local French ex is also interesting.
(iv) A different term might be useful, because "reduced relative clause" is ordinarily used for nonfinite relatives. Cf. Keith & Brown, Dictionnary of linguistics, 2014:
REDUCED RELATIVE CLAUSE A relative clause in which the relative pronoun or subordinating conjunction has been omitted, along with some form of be. E.g. The guy who was repairing the leak has gone reduces to The guy repairing the leak has gone.
A "headless relative" might be useful, although it is not ideal either, as it standardly refers chiefly to free relatives.
(v) Theoretically it may be worth highlighting that this is, as far as can be told from the descriptions, a "construction" in the sense of Construction Grammar: bet seems necessary, e.g. no Me a vo hag ez in da gerc'hat amann da Rosmeur.