I have been through the same scenario now three times. Very frustrating.
The first two times the voltages measured about the same as you are seeing, 13.4 to 13.6 at idle, but still my brand new battery would go dead at irregular times.
Turned out it was the battery, had a dead short in both of those batteries. The short was intermittant and did not show up with the electical testing at first. The short did show up soon enough when the battery went 100% dead as I was driving along. The only way to test for an intermittant battery short is to get it out and in the clear, then tilt it away from everything and remove the caps.Run a jump across the two posts. If there is a short the cell that has the short will fizz up like a geyser. Needless to say this is not a safe and sane test, but desperate times...
Next time it was the alternator. Similar problems with intermittant contacts, as they will test just fine, but will fail to work at other times.
You might try removing the battery cables and see if the battery stays charged. Do it on a Friday night when you have some time. If it goes dead with nothing hooked up it is the battery.