I've checked several times on the DPS website, hoping to receive some indication that it was in processing, but no joy. I started to think that perhaps they had not yet received my documents. As of yesterday, there was nothing on the site to indicate they were working on it.
Then, today, I checked the mail and found it had arrived - and there was much celebration.

Now that I have my new LTC in, I guess it's time to retire my old CHL to that folder in my safe where I keep all my expired & full passports, etc. That old card served me well, and still had a few good months left on it; but it has earned its retirement in CHL Valhalla: inside my safe, next to the guns that it empowered me to carry (and a few others as well).
Next step: renew my wife's card this month so her old card can enjoy retirement alongside mine.