OK - finished the tests .. The temperature is 0C (32F) and the Enclave had been sitting outdoors for 2 days. Without putting in the key in the ignition, measured the voltage at the remote terminals and the battery as 12.2V. With the key in the ignition and the radio on (one click up). The voltage dropped to 11.9 V and the "Start Vehicle" message went on (within 2 minutes). I left the radio on for about 5 minutes and the voltage didn't drop below 11.9V. I started the car and the charging voltage was 15.1V for about 2 minutes. After ignition off it was in the 12.3V range and dropped slowly .. I turned the lights / radio on and it dropped to 11.8V and the "Start Vehicle" message came back on after 1 minute. I did this test about 5 additional times. I didn't let the car run for more than 2-3 minutes between powering off. Each time the battery voltage dropped below 12V, there was about a minute delay and the message appeared to start the vehicle.
Just for reference I measured the AMP draw from the battery and it was about 1 AMP with the interior lights on No Key. 1.7 AMPS with the key in and radio on. 10 AMPS car running.
A light load on the cold battery measured 12.2 volts. Radio / Lights caused the battery Voltage to quickly drop to 11.9 which was enough to cause the message to appear. The key point was even with the radio running for 5-10 minute period it didn't drop more than 0.1 V from 11.9V , so it appears that the threshold is just slightly above what the battery is putting out (when cold). I tested the battery voltage disconnected from the car and it was 12.7V. I also used an Ancel BA301 battery tester and it reported the battery as good when disconnected from the car.
I don't know if there is a solution, but it doesn't look like the "Start Vehicle" message is a good indicator of battery capacity or health. It looks like the draw on the (cold) battery is enough to drop the voltage to below the threshold where the message appears.
Hope this helps.