Re: EZBL half-duplex UART over single wire
There's a multitude of options available.
I'd suggest to check whether a sample configuration for LIN is available/documented, which has exactly the same challenge.
(Only) If not, my personal preference would be to (dummy) read the RX register each time I TX a byte - plus one more time prior "switching" to RX. The PC side might be different, or you modify the PC's interface such that RX is disabled when transmitting. (Can be done in a number of ways.)
PEBKAC / EBKAC / POBCAK / PICNIC (eventually see en.wikipedia.org)