I work with PICs so what I might try may not be available in your micro. On PICs, at least the ones I use, there is a separate bit for enabling the UART transmitter and another for the receiver in one of the control registers. Since the TX line idles at a high state (that's why you can't tie them together), I would disable the UART transmitters on the slaves and set the pins to an inputs so they float. The Master would query the slave and when the slave was ready to respond, it would enable the transmitter, send the response, then disable the transmitter again. This should work if the slaves didn't have to initiate a request.
I haven't tried this scheme so I'm not sure if will work. I have designed circuits with multiple processors and I just picked a micro that had 2 UARTS to be the master. It made it much simpler but I also had the requirement that the slaves could query the master. 2 UARTS made it easy.
Another option is to add an open drain/collector buffer on the slave TX pin and wire-or them. With a weak pull-up on the master, the slave should be able to pull the TX line low when needed even if the other slave is holding it high.