Riva:
I'm wondering if I can power the TX modules at more than 5V, let's say 9Volts, in order to increase TX range.
I have not seen a datasheet to check if this would increase RF power but normally countries only allow these free spectrum devices to work up to a specific output power and this may be fixed within the chip.
Presumably, the transmitter radiates the maximum legal ERP at 12V. At lower voltages, it probably radiates less.