I looked into this a while back, a post about is Arduino Due comms problems on programming port The Due design has had a few changes, but I don't think a change log is publicly available.
The old Due design had #OE connected to ground, so that the driver is always enabled. The idle state of a UART is High. As you found, this can prevent re-use of Serial0.
At some point the Due design was changed to wire #OE to it's input pin, so that it is only driven low. With the Atmega UART in the idle state, the '125 buffer chip is High-Z, allowing re-use of Serial0.
Because Arduino don't label versions, and anyway don't have control of clone makers, the only way to find which version of Due you have is to examine it under a microscope. I'll bet you have the earlier version where #OE is connected to ground.
I actually had the opposite problem, with '125 buffer in a High-Z state, there is only a weak pullup on the RX line, so higher baud rates didn't work reliably.