Thanks for sharing..
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Maybe You can increase the amount of data in each burst just to see if the device fires the "SEND OK" earlier based on some ESP8266 buffer used limit.
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Also check if the ESP8266 has some TCP package size that may affect sending.
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Since You obviously have full control of the server it can be interesting to see some timing on when data hits the server after you have sent the negotiated number of bytes to the ESP8266.
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Try some of the other WiFi devices from the new Espressif product range to see if they all work the same.
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Finally, if nothing helps, try to have the server send back some dummy, out of protocol data as soon as the first character hits the server. Unfortunately the receiving end of your application will have some garbage but just read on until you find valid input.
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