You didn't say how you got on but anyway, in the mean time, I have got hold of one of the boards mentioned back in post #82.
It would replace most of your modules (power supply, relay module, microcontroller board) leaving you to supply only a separate RFID reader and two LEDs. For this specific board you'd have to upgrade the software because it is ESP32 based but usually that means merely swapping out a library or so. The wiring and assembly would be much cleaner and the board is only 80mm x 45mm and breaks out most pins.
I did a short write-up here with some sample code: ESP32 WiFi Bluetooth Single Relay module sample code