I would ask about a CoughAssist and oscillating therapy vest. There are a couple of different options now. The Vest breaks up the secretions and the CoughAssist basically uses deeper suction to get them up. These are not right for everyone, but may work for you from what you describe.
There aren't any numbers on the report snippet you posted (feel free to add that part, but please redact your name -- I did that for you) , but if you are chronically short of breath, I would also ask about BiPAP.
There is a device that combines suction, BiPAP, and the CoughAssist (but not the vest) that could be worth trying if it turns out the CoughAssist works for you without needing the vest. It is called VOCSN. Don't know if it's available through the VA.
To keep things moving meanwhile, hydration is good as you are doing, but you could also experiment with warm lemonade and the like, to see if one kind of liquid helps get out the gunk better than others.