First, thanks for your service. Ex-NAVY myself.

I think the ultimate answer is gonna have to be a different bike/wheel combination. More relaxed geometry combined with wider, softer commute tires is in order. Yes, you might squeeze in a fatter tire on your Schwinn. And it would still have the same tight geometry. The tires would help but strike me as only half way their.
I generally suggest a cyclocross design of some sort, or one of the cafe bikes, with drop bar ends added. I like the Jamis 'Coda' or Motobecane 'Cafe Noir', to name just two of this sort.

These will accept tires in the 28-32mm range and have a slightly longer frame, often of steel. This makes them more forgiving over rough terrain. And who can refuse owning one more bike?