Use Theme with appropriate construals as needed.
The postposition [p hi/को] optionally marks a Theme only when there is some prototypical Agent involved in the action. That Agent isn't necessarily even named in the sentence. There is also evidence that the optional [p hi/को] marks more salient or definite objects (e.g. it is not optional on animate objects).1
Use Agent↝Instrument (or any of the other relevant ने scene roles).
The impelled agent (मध्यस्थ कर्ता) is a mediator forced to do some action by a full Agent (marked with ने). They lack the volition of the full agent. This construction involves a second causative verb.
'I made the maid put the child to sleep.' 003
First of all, the function is undoubtedly Instrument since it is an entity applying causal force. Now what reasoning is there for the scene role not being the same? Well, if an actual Instrument is used to perform some action, the second causative verb is ungrammatical. A first causative verb is used when the intermediary has no agency at all.2
'I opened the lock with the key.' 004
'I made the owner open the lock.' 005
So it's not Instrument↝Instrument. That is why I have settled on using Agent↝Instrument as the construal, since it captures both the impelling and the agency encoded in the construction.
The problem is that instrumental agent does not perform the action with volition. However, I don't think volition should be considered in the formulation of SNACS as it stands. My thoughts below on modal and passive constructions will support that opinion.
Magier, David. "The transitivity prototype: evidence from Hindi." Word 38.3, 1987. 187-199. ↩
Begum, Rafiya, and Dipti Misra Sharma. "A preliminary work on causative verbs in Hindi." Proceedings of the 8th Workshop on Asian Language Resources. 2010. ↩