You should be able to do what you are describing but it will require a custom application and it may still be a bit tricky. The first thing to recognize is that POM is basically an "IVR that calls a number" instead of an IVR that takes calls. That means that the VoiceXML application invoked by POM can be any IVR application that can be created for the Experience Portal. Assuming you can create an application that can successfully navigate those third party IVR flows, then POM can use that application. Also, if there are multiple IVR flows to navigate, your custom application will have to be able to tell which IVR flow it has to navigate and then do the "correct" things. Although the custom application part will be tricky, there are also the following potential issues.
You should not be surprised that POM classifies the IVR interactions as AM. It is correctly determining that a non-human device answered the call and separating that from a person answering. Since POM makes it easy to do different things for AH and AM, that is actually in your favor. You can have your AH VoiceXML application be different from the "custom" AM application. If this is an agent-based campaign, the AH calls will go to agents and the AM calls will go to your custom app.
There are two cases where you may still have some hurdles to jump. If the campaign is an agent-based campaign and you want the custom application to "navigate" the third party menu tree FOR the agent, I'm not sure how to best do that. Your custom application could transfer to an agent, but that's a slower way to get to an agent than when POM immediately connects an agent to an AH condition.
The second challenge I see is if you need to leave a simple answering machine message on regular answering machines but do the more complicated navigation of third party IVRs. Since you will have to figure out some way to have your custom application know WHICH IVR flow to follow, it may be possible to have it recognize that it was invoked for an answering device that isn't an IVR and to simply play an answering machine message.
Hope this helps and good luck.