LakeErie, I am little over two years post surgery. I went through three laryngoplasties (VC injections) to allow me something of a voice and the ability to swallow thin liquids. The improvements you note are very similar to what I went through,
The coughing is still present, although it is nowhere near as prevalent. In my case, the cough is a result of the loss of autonomic swallowing, peristaltic action of the small muscles in the throat. Any mucous, including the normal mucous that coats these passageways, just gets stuck and needs help. Dry foods I still struggle with and have to be careful. I drink a lot with meals.
However, things are so much better. In normal environments, at normal volume, my speech is normal, with some coughing. In louder environments, not so much. As you have probably noticed by now, your body tries to pitch your voice differently and with greater volume - regardless of your intent. I think also that SSD compounds this. Again though, I have significant improvement. I still can't sing more than a few a bars, and it seems I will never sing tenor again, but that's okay.
It is very difficult to be always be patient, but it seems to be what we need.
Best to all,
tod