Determining UART RX pin "blind"?
Use a multimeter in continuity test mode and verify which of the remaining header pins connect directly to the 3.3V power supply. Probably only one does.

With those set aside, the remaining ones that you originally measured at 3.3V will be either inputs with a pull-up resistor to 3.3V such as RX or CTS, or an active high output such as RTS. 

For whichever pin you feel is likely RX, put a 1K ohm resistor in series with your Pi's TX output to limit current in case the pin you are testing is in fact an output and try it out. When you are sure you've identified RX after your test then you don't need the resistor anymore.