That test results clearly show that the turn-on delay is absolutely necessary. Why not give your Txer more time to wake-up?? Say 100ms and test how it goes. Then you can decrease this wake-up time gradually.

Also if you send a long stream of preamps and only 1 or 2 data bytes, that is OK. No manchester is really necessary. But more than this... don't think whether to or not to. Just add it.

More, I would suggest for 100% reliable communication to add checksum or even better a CRC check.

Almost every receiver will output noise that could lead to false data reception when no transmission takes place. There is no mute function available on these cheap devices.

Ioannis