I'm thinking about trying to use an esp8266 again.  I switched to the esp32 because software serial at 9600 baud gave a lot of watchdog resets, not what you want in a time server.  Software serial was needed because the esp8266 has only one usable UART and that is used for programming and debug messages.  It has a second one but the receive pin is in use by on module flash making it unsuitable for receiving messages from a GPS module.

   I've found that its possible to swap the pins used for UART0 to an alternate set of pins and I can connect the GPS there.  You can also send debug messages to UART1 since its transmit pin is usable.

   I'm interested to see  if the GPIO interrupt latency is more consistent than I have found on the ESP32.  There the latency varies between 4us and 38us.  With wifi connected it tends to be on the higher side.  With two cores, wifi using core0 and my app and GIPO interrupts using core1 I expected the ESP32 to be able to respond consistently.