I figured it out!!

Seems killing the screen session doesn't properly disconnect. After putting the UART into transparent bridge mode you must explicitly quit screen by issuing:
Ctrl-A
Ctrl-\Alternative to using 'screen' to connect to Bus Pirate, you can use 'cu' as well.
sudo cu -l /dev/cu.usbserial-******** -s 115200
# (******** is the Bus Pirate serial number)When using 'cu' it will get a hangup signal as soon as esptool.py starts up so you don't need to manually disconnect or quit.
Then the correct output of esptool.py will be:
Connecting...
Erasing flash...
Wrote 4096 bytes at 0x00001000 in 0.4 seconds (78.8 kbit/s)...
Erasing flash...
Wrote 271360 bytes at 0x00002000 in 29.7 seconds (73.2 kbit/s)...
Erasing flash...
Wrote 259072 bytes at 0x00081000 in 28.3 seconds (73.2 kbit/s)...
Erasing flash...
Wrote 4096 bytes at 0x00101000 in 0.4 seconds (82.0 kbit/s)...
Erasing flash...
Wrote 4096 bytes at 0x00102000 in 0.4 seconds (78.8 kbit/s)...
Erasing flash...
Wrote 4096 bytes at 0x00202000 in 0.4 seconds (82.0 kbit/s)...
Leaving...
So, in summary, the steps in my second reply work, provided you hit "Ctrl-A" then "Ctrl-\" to quit screen after putting BP in UART transparent bridge mode.
Since this is specific to Mac, I've edited the title of the thread.