Okay... Quick update:

1. In the time between the first post and now, the trickle charger went from yellow (charging) to green (charged), so the battery itself is probably fine.
2. I had my wife listen while I cranked and after I explained where the clicking noises can originate, she concurs that it is the solenoid, not the relays on the driver's side under the hood or under the dash (noise is coming from driver's side engine bay, and is quieter to me with door shut)
3. New symptom: Unlocked with fob, alarm went off. Fortunately for neighbors I have one of the bum alarm units that you can't actually hear with the hood closed (and with the hood open, it sounds like an angry mouse)
4. New symptom: When locking with key fob lights were VERY dim.

Conclusion: I concur that is likely a bad cable, now just to find out which. There was a lot of corrosion on the old battery negative terminal. I cleaned the connector before installing the new battery, but could these symptoms be related to negative cable as well as positive? If so, I have no issue with making that my next troubleshooting step. Just so I don't have to dig, do you know off the top of your head where the negative cable terminates to the frame/body?

Also will try disconnecting my audio system, as it has 4ga wire tapped directly to the battery. Just one more thing to complicate an already complicated system...

Thanks for the quick feedback!