Might be good to read the data from the buffer and store it in your own "buffer" so the FIFO buffer doesn't get fulled.

[Codebox]
l_count = 0;
l_length = 0;
get_us = esp_timer_get_time();
stop_us = INTERBYTE_MS*1000;
while((l_count==0) && (l_size < reply_limit))
{
l_length = uart_read ...