I ended up getting two different power supplies rated at 12V 1A (12W). The first one didn't work... the lamp came on but exhibited strange behavior. Once on, the controls stopped responding. No undue heat or smell of any kind and the lamp function went back to normal once I put it back on the original power supply.
The second one... was a winner! Oddly, same listed specs, but the lamp accepted it and worked fine. It's a higher quality power supply with nice sturdy casing and thick wiring. I don't know if there is something substandard about the first one, but it was cheap enough ($2.50) not to bother me. The good one was $4. Well worth it, as it's a slimmer, more tastefully designed power supply than the original one (even if it had a US plug).
As for programming the Mi Home app... still went nowhere with this. I got further using an old 5th generation Apple iPod Touch. In the iOS version of the Mi Home app, I was able to detect the lamp's WiFi signal and data was passed such that the lamp indicator changed from flashing amber to solid blue. That means it found and attached itself to the in house WiFi network. Yet... the Mi Home app had a "time out" when attempting to finish the connection. The app still doesn't have the device registered, so there's no way to control it remotely. At least the flashing amber LED issue was solved. In a dark room, you could see it. No doubt, a little piece of electrical tape covered over it would do the trick... still--nice to know the lamp actually could get onto the WiFi. Now the hope is that a future version of the Mi Home app will solve this issue. It's not a deal breaker... the lamp still works great. I really like it.
UPDATE: I was able to make a little more progress on Android. I have an older HTC One M8 running Marshmallow Android. I was able to get the Mi Home app installed and it found the lamp. It was able to successfully pass WiFi info to the lamp and it responded. However, the final task was for the Mi Home app to bind to the lamp by showing it as an added device. It failed to do that. I did see a message to "bring lamp closer to router", but despite doing that, just 10 feet away, I had the same problem. I confirmed the lamp has the correct info, by changing the WiFi name. As soon as I did that, the status LED on the lamp started flashing blue. Then, once I changed the WiFi name back, the LED stopped flashing and remained solid blue (with no network info, it would flash amber). So, the lamp is on the WiFi network. My hope is that a future version of the Mi Home app will possibly address this issue. I've notified Xiaomi.
My only other gripe is that there's no emitter tint adjustment. There are some LED lamps that offer this, simply by providing multiple banks of LED's grouped by CCT range. The neutral white tint is OK, with just a touch of green. I tested a minus green filter on it and it was a nice shift that had minimal impact on overall output. So I'm going to carefully cut an ellipsoid shape of the filter and use an adhesive specially designed for attaching tempered glass protectors. It should be good enough to look natural.