The expirment most likely means there is a bug with the FSK T/R pair.
You can easily overcome this by sending your data in 2 bytes such that the "code" b'00000000' is never present in any byte.
That requires a mod of the software, but quite a simple one:
the 8 bit "variable" holding the leds state should be updated and fed to the leds only after 2 bytes where recived and "decoded"(assuming it is important to chnage the leds from one state to another at the same time).
Btw,
If possible, talk to the manufecter/report the bug.
About the range,are you using the proper antennas?