In response to your responses (and thanks for those, by the way):
a) I'm typically parked on level ground.
b) The dealership also checked the fuel pump, starter, alternator, etc. I did end up replacing the evap canister in addition to the battery and cables.
c) The engine's non-start condition seems to alternate between the security non-start meaning engine won't do anything and the dead battery start meaning it turns and clicks.
Okay, here's the update.
After a week or so with the new battery and cables it did it again. I got stuck at the doctor's office yesterday. Turn the key...nothing. I put a portable battery charger on it, still nothing. So, the receptionist sees me out there and pops her head out and tells me to put it in neutral and roll it forward then try it. I do this and it starts immediately. She tells me that she had a Suburban with the same issue. They could find nothing wrong with her vehicle but if she charged it, shifted into neutral, and rolled it the truck started. She told me that this became her everyday process so she traded it for something firmly outside of the Yukon/Tahoe/Suburban/Denali/Escalade family. This saddened me a bit, as this Denali is kinda my dream vehicle. I thanked her, bought her lunch, and limped off.
While trying to get this thing going, I called the dealership which was right up the street. They told me to bring it back as they now suspect some kind of "parasitic draw" (their words) causing a voltage drop. We'll see...
This is getting expensive.