Since this is your first installation, I’m going to say a few things that might seem elementary. I’m not trying to be condescending, I just want to make sure we’re all working from the shared understanding of how the system works.
First, Asterisk is a Back-To-Back User agent. All calls are a two-step process. That means that calls come in to the PBX and new calls from the PBX are created for the outgoing “leg” of the call. If you approach the problem with this perspective, all calls to your local phones are internal. This could be part of the issue you are seeing - anytime your GS phone is talking “to the world”, regardless of direction, it is always talking to the PBX in a local call.
Part of your description of the problem confused me a little bit. It sounds like you want to have to ring tones on your phones - one for internal calls and one for incoming calls from outside. This is handled through the “Alert Info” settings in the various parts of the system. Now, I’m no expert in Alert Info settings (I work a lot with Cisco phones using SCCP, and we handle that differently, see note below), but it seems to me that just about every phone has its own “way” of handling Alert Info.
Now, that only handles the “ringing on the desk” part - when the phone is just sitting there and starts to ring. The other part of the call (what you hear in the handset when the other phone is ringing) pretty much always stays the same. I’ve never messed with this, so there might be magic in the system somewhere that handles this, but I wouldn’t have a clue where to look for it.
One thing I have heard about the Commercial EPM is that the Alert-Info settings are only ‘filled in’ for Sangoma phones. The Alert-Info settings in EPM will not work with Grandstream. Now, there’s been a lot of discussion about this in the past, so this “feature” might have been updated lately, but if now, that could be holding you back.
Finally, knowing that Alert-Info is how the system tells the phone which Ring Tone to use, we’ve had lots of discussions here on the forum about Grandstream phones and Alert-Info. On the downside, that means that you’re going to have to slog through a lot of posts to find one that talks about what you’re doing. The upside: it puts you in really august company, because some of the smartest SIP people I know have wrestled with this issue on GS phones.
One final wrinkle - the Alert Info handling in FreePBX/Asterisk was changed rather significantly about 18 months ago, which screwed up a s-ton of working phone systems. If the articles you are using for information are older than that, this could be biting you as well.
Promised Note: On the Cisco phones, you have have up to nine (IIRC) different Ring Tones, which are managed in the RingTones.XML file. The XML tags in that phone file match the ring tones to the incoming Alert Info from the system, allowing for a “Default” ring tone (which is used to anything that doesn’t come in from somewhere that sets Alert Info) and allows for a bunch of other Ring Tones that alert the user to the source of the call (Inbound Routes can set them, as can Ring Groups, Queues, and other parts of the system). This means (for Skinny Cisco phones only) that the Ring Tones file can be modified to match what the phone system is sending - a feature unique to this particular phone configuration.