If you can't find a better way to figure out how to make the 201 work, I would try to power on both and measure voltage on each pin of both chips (prepare a steady hand). The voltages might not necessarily need to be the same on both boards in order to make it work but it might give you some hints (or not).
To communicate after flashing keep IO15 pulled low.
I upgraded to ai-thinker V0.9.5 that's been modded with GPIO and ADC commands, works great.
Have the device booting. Baud rate pre set at 115200.
Have not tried to flash a firmware yet though.
Comes up as:
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ready
AT
OK
AT+GMR
0019000902
OK
I assume the garbage is Chinese. I am using the Arduino serial monitor which I believe cannot display the characters correctly.
I had thought the mini antenna would have increased the signal strength but it does not appear to be any better than the 01 module.