There's a simple way to "or" the slave TX lines with just one resistor.
Just tie several open collector outputs together and use a single pullup
resistor.

Almost all Microchip I/O pins can be configured as open collector.  Set
the data register to 0, and write the data to the direction register.
When the data is "1" the pin is tri-state, when the data is "0" the
output pulls low.  I've used this method to tie several Dallas 1-wire(tm)
parts to a single I/O pin.  That's why they call it 1-Wire!

Such a configuration is not high speed compared to RS-485, but it could
go at 19.2 kBaud over 20 meters without even really trying hard. I've
worked it at equiv to 9.8 kBaud at 300 meters.   With 2 or 3 line
protocols you could go significantly faster.  Is 19.2 kBaud fast enough?