Hello Will,
Hope you are doing well. I have reviewed the USART module that the LPC54114 has and unfortunately there is not a register that will help with the timeout value directly. So this will have to be a custom implementation. I think the main idea that you should consider is using the RX interrupt as well as a timer. So you can work with both simultaneously if the timer causes an interrupt first then go ahead and read the FIFO. The RX interrupt can cause the timer to restart or if FIFO is full before your timer causes an interrupt it will also allow you to read it at that point.
It all really depends on how you would like to implement it, but I recommend checking Chapter 15 and 16 for the timers.
Start with the examples provided in the SDK with a normal interrupt and add the timer concept described above.
If you have questions about the implementation or it is not working how you are expecting please let me know with the adjustments you made so I can check it for you.
Best Regards,
Sabina