Hello again.
From the first time i read these posts, i was sure this sensor could be hardware modified to be improved. So i started researching and finally i modified that.
First, i used 3.3V DC power, buck converted from 12V via a step down regulator. Directly to the ESP8266 pins, bypassing the co-processor.
Then i connected another PIR sensor ideal for 3.3V. AM312 is the type. I also connected its power to 3.3V and the signal to GPIO2 on the board.
I also connected a blue led on TX and GND in order to replace LED functionality.
Now the PIR sensor responds rapidly and sends MQTT messages immediately as it is always on consuming about 80mA on 3.3V. I use Tasmota as the firmware choice and i attach also the template which is based on Sonoff Basic
I hope i helped a little.