Yvonne, unless I misunderstand you, I would think that you're still not entirely correct. In one thing you are, however: the answer to your question is, indeed, quite simple, however much Episcopus' lenghty dissertation concerning the object of your question might lead one to suspect otherwise.
Regardless, you're correct in discerning two types of participles: active and passive voice. Sometimes (for example with the verb: induere) the passive participle has a reflexive meaning, in which case it resembles the (Greek) middle voice. Yet, we may discard this for now, I think.
However, there is, unlike you -if I read your words correctly- suppose, no relation between the voice of the participle and the case of the noun with which it agrees. In fact, any participle, be it active (praesens/futurum) or passive (ppp, and gerundive) may congrue with a noun, which noun may be the subject, the direct object, the indirect object, but it may stand in the genitive and ablative [which, in that case, needn't be an ablative absolute] as well!
The choice between an ablative absolute and a participle in agreement (not being an a.a.)depends on two factors, which, being both
the case, decide the matter in favour of the non-a.a. participle. The first: the noun, whereupon the participle bears, is already present in the sentence. The second however: the participle needed must be one of three
, namely: a. praesens active (eg: vocans), b. futurum active (eg: vocaturus), c. perfect passive (eg: vocatus). If a different participle is needed, such as a perfect ACTIVE, then we must note, that Latin lacks this participle (except for deponents). In that case, the a.a. may fill this syntactical gap.
To make it more clear, regard your sentence D -> ...we left the camp and advanced against the enemy. ...castris relictis in hostes progressi sumus.
As you see: "we left the camp" would require a perfect ACTIVE participle, yet "relinquere", not being a deponent verb, lacks it. Therefore, although there is a subject with which the participle might agree, it is lacking in the needed form. The a.a. forms a substitute. (strictly, "castris relictis in hostes progressi sumus" means: "the camp having been left, etc." That the act of leaving is performed by, in this case, the subject, is merely a convenient inference). If however the English would be: "when we were about to leave the camp, the enemy advanced against us" we would get "hostes in nos
castra [object of participle] relicturos