Consider participles that are not marked for voice at all. (Note: the English past vs. present participles are rather passive vs. present, although the way English participles work is a bit more complicated than that.) Now, such participles could behave in different ways depending on how we want to structure the language - animacy hierarchies, for one, could be a very natural approach to how to parse them.
However, let's go for something less obvious, but still pretty obvious: let's have the case role of the NP with regards to a finite VP also double as its role for the participle:
the man sold the castrate-PTCPL horse:
horse is the object of sold, so it's also the object of castrate, thus:
the man sold the castrated horse
the travel-PTCPL man made a bid:
man is the subject of offer, and therefore also of travel, thus:
the travelling man made a bid
What can we do with this? One obvious potential restriction could be one of only permitting this to work for arguments – non-argument adverbials and such seem less likely to have their 'role' passed on to a participle.
A second thing we could do is make the role that is passed on to the participle be less carefully differentiated - maybe not distinguishing objects from indirect objects or somesuch.
Here, a light ergativity could be introduced: intransitive participles could be accepted as 'active' participles for objects of transitive verbs.
To make the system more flexible, one could use resumptive pronouns in the desired case, which could lead to a neat way of turning case markers into voice markers.
I had an idea on ergativity and participles, that I have since forgotten. I am hopeful that I might be able to reconstruct it fully and post it soon enough.