Linking Mulitiple Arduino's
Why do you need so many Arduinos, Nanos and a Mega?  You want to read/control 2 joysticks, some switches and some LED.  If you do this using a multi-processor environment then you are adding a significant overhead to the processing and the development time which you can probably do without.

So, could you connect everything to a Mega, do you have enough IO pins?  If not would the use of GPIO expander ICs, I2C devices, etc help solve this issue.

Connecting the joysticks via interrupts will allow a more responsive system, can you do this?

Is an Arduino even the best platform for this?  What about an ESP32 or PI?

You want to minimise the comms overhead, so a star network would be better than a ring.
Serial is going to be the lowest programming overhead solution, but by far the slowest.  Using WIFI via an ESP8266 is going to be the simpelist and you can hand off some of the processing to the ESP.