Hello Shane,
What board are you using? It should be working with those lines that you added. I took periph_clkout example from LPCOpen (LPCXpresso 11u68 Board Rev C) and made next modifications on main function:
SystemCoreClockUpdate();
Board_Init();
Board_LED_Set(0, false);
/* Enable clock for RTC */
Chip_Clock_EnablePeriphClock(SYSCTL_CLOCK_RTC);
Chip_Clock_EnableRTCOsc();
Chip_Clock_SetSystemPLLSource(SYSCTL_PLLCLKSRC_RTC32K);
Chip_Clock_SetMainClockSource(SYSCTL_MAINCLKSRC_PLLIN);
/* Enable and setup SysTick Timer at a 100Hz rate */
SysTick_Config(SystemCoreClock / 100);
/* WDT oscillator freq = 0.6MHz divided by 64 = 9.375khz */
Chip_Clock_SetWDTOSC(WDTLFO_OSC_0_60, 64);
/* Enable the power to the WDT */
Chip_SYSCTL_PowerUp(SYSCTL_SLPWAKE_WDTOSC_PD);
/* Configure PIN0.1 for CLKOUT */
Chip_IOCON_PinMuxSet(LPC_IOCON, 0, 1, IOCON_FUNC1);
/* Setup CLKOUT pin for specific clock with a divider of 1 */
Chip_Clock_SetCLKOUTSource(SYSCTL_CLKOUTSRC_MAINSYSCLK, 1);
while (1) {
}
Then, I was able to measure the 32.768 kHz on P0.1 pin:

So you can give a try to do same modifications on periph_clkout example.
Hope it helps!
Regards,
Isaac