Hi Phil
If pull-ups are enable on the UART receiver lines this represents a load of between 20..50k for each slave - probably around the 20k end on average. 10 slaves would make about 2k, which is still not low impedance for the transmitter.
If you use low power mode you should find this define:
#define UART_PULL_UPS (PORT_PS_UP_ENABLE) // activate pull-ups on UART lines to avoid them floating in low power modes (which causes leakage currents to flow)
If you comment it out the UARTs will not use pull-ups.
Also check adding additional resistors to see whether there is a limit to the drive level.
To use higher drive strength at the Tx change
#define UART_PULL_UPS (PORT_PS_UP_ENABLE | PORT_DSE_HIGH)
in case of drive problems I expect that this will be seen at the scope as bad logic levels or slow slew rate.
If you work in a polling environment are you sure that there is not a problem with the polling cycle time when the number of slaves is increased rather than an electrical issue?
Regards
Mark