Thanks for the suggestions. I chose to take it one step at a time, so I first turned off the power nap setting.
Although it appeared to improve the situation; i.e., every time I let the notebook go to sleep, I was able to wake it up. Only once did I have to press the power button to wake it up because the trackpad nor the keyboard would do it. But it did wake up as expected.
Unfortunately, just a few minutes ago, I woke it up again just to find out that it had actually rebooted due to the following problem: panic(cpu 0 caller 0xffffff801c816487): "ATY,Boa::setPowerState(0xffffff86b1dff000 : 0xffffff7f9fdb6d88, 2 -> 1) timed out after 45940 ms"@/AppleInternal/BuildRoot/Library/Caches/com.apple.xbs/Sources/xnu/xnu-6153.101.6/iokit/Kernel/IOServicePM.cpp:5296
Obviously, there's still some power-related-problem lurking inside this $5K machine of questionable reliability. So sad.
I'll try to work on your second suggestion tomorrow.