The question is on the highlighted sentence in this opening paragraph of Le maître Chat ou le Chat Botté as collected by Charles Perrault.
Un meunier ne laissa pour tous biens, à trois enfants qu’il avait, que son moulin, son âne et son chat. Les partages furent bientôt faits ; ni le notaire, ni le procureur n’y furent point appelés. Ils auraient eu bientôt mangé tout le pauvre patrimoine. L’aîné eut le moulin, le second eut l’âne, et le plus jeune n’eut que le chat.
Am I right to understand the sentence as follows.
auraient eu mangé is not a conjugated (or finite) form of manger.
Rather, mangé occupies the same grammatical position as does on the table in this sentence:
Ils auraient eu bientôt sur la table tout le pauvre patrimoine.
From the sentence, we don't find out who would have eaten the patrimony. We only learn that a notary or a lawyer would have caused it to be eaten perhaps by some third party. (If we thought the notary or the lawyer would be the one to do the eating, that would be a guess, not what the sentence says.)
The following formulation would however tell us who would do the eating, namely, the notary and the lawyer themselves.
Ils auraient bientôt mangé tout le pauvre patrimoine
If possible, I would appreciate an answer that takes each of these four items and confirms or denies it.
Please forgive 2 being non-sensical. If I knew how to say tied up in litigation in French, I would have said that.