Alright... I've been in constant conversation with both Apple and my service provider.
I spoke to an individual who used to work for the SP, who now works as a manager at an Apple store. He's helped quite a few people who have had this incident; and all of these people are with the same service provider. What he suggested is that the individuals call their respective service providers and ask for a reset of the network connections... NOT a reset connection from the Iphone, but rather an entire reset of the network and the number attached to it.
What this requires is essentially (depending on the provider) up to 72 hours waiting for a complete reset of the network. It has worked with every individual he has helped. I'm in the process of waiting right now.
This isn't exactly an Apple problem, nor is it a Service Provider problem. What I have found is that, when the phone restores to factory settings and a complete and fresh network reset has occurred due to a completely "new" Iphone connected ("new" as in a completely reset to factory default settings), it works. However, as soon as there is severance between the phone and the network, this problem occurs. This could be leaving the phone in Airplane for a short period of time (i.e. 10 seconds or longer), or when the phone is shut off, or when the sim card is removed, or (in the cases I have used frequently) the battery has drained completely. This would explain why individuals who receive brand new Iphones are still having the same problem occur.
Therefore it's a network connection issue. Because the phone simply perpetuates the "calling" act, the handshake between the phone and the network isn't being dealt with. Either the network is not accepting the phones handshake to begin and end network usage (I.E. messages or phone calls), or the phone is not accepting the networks attempt to engage in a phone call. That would explain why people may hear you ring their phone, but you cannot speak to them nor they speak to you.
Finally, what this means is that the Phone App has a glitch or bug that occurs due to an unforeseen error during the "handshake" between the network and the Iphone. The reason the service providers want to blame Apple is because on their end, the calls are going through. Apple wants to blame the service providers because it's clearly a network issue, and that belongs to the network providers.
TL;DR....
This issue is one that involves Every service provider whom this happens with, AND APPLE. When Apple allows an SP to advertise their product, they are essentially endorsing that service provider as being capable to handle such a product. On the other hand, by advertising the product, the service provider is guaranteeing that the product works on their network. Thus, a dialogue must open up between both Apple and the respective service providers so they can rewrite the Phone app Code and be prepared to reset networks in the instance such an issue arises again.
I'm in dialogue with both my SP and Apple everyday now and I've spent 12 hours cumulatively speaking to them in the past two days. I WILL ensure something more concrete will be done.
Until then, everyone try calling your service provider and asking them to reset your network. Explain your phone problem and tell them that a network reset from the phone is not enough, what is required is a tier 2 reset (meaning a reset from a person higher up than your average tech support staff).
Good luck. I'll keep posting as I get results.