I was unable to find any support APIs (such as HAL_Read_UART_Config()) and ended up inserting the following code:
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// Taken from fsl_uart.c (around line 315)
// Set tx/rx FIFO watermark
UART0->TWFIFO = 0;
UART0->RWFIFO = 1;
// Enable tx/rx FIFO
UART0->PFIFO |= (UART_PFIFO_TXFE_MASK | UART_PFIFO_RXFE_MASK);
// Flush FIFO
UART0->CFIFO |= (UART_CFIFO_TXFLUSH_MASK | UART_CFIFO_RXFLUSH_MASK);
// Enable receiver RTS(request-to-send) function.
UART0->MODEM |= UART_MODEM_RXRTSE_MASK;
// Enable transmitter CTS(clear-to-send) function.
UART0->MODEM |= UART_MODEM_TXCTSE_MASK;
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This pulled the control lines to their correct values and the serial link is now operational. In order to "de-initialize" these lines, the last two lines of code become:
UART0->MODEM &= ~UART_MODEM_RXRTSE_MASK;
UART0->MODEM &= ~UART_MODEM_TXCTSE_MASK;