The printer and LCD do not send any data back to the CPU.

In that case, you could try a soft UART-approach. UART TX is fairly simple to do in software - RX would be a lot more complex.

Whether this is feasible depends on your system (available CPU time, etc).

If a printer or LCD sees garbage would it try to print or display that garbage or would it simply ignore it because of the baud rate error?

A UART cannot detect a baud rate error. It can detect some other errors (parity, framing). Whether the LCD would print garbage or ignore the byte would depend on whether one of these other errors occur. If you send just the right (wrong) stuff to the high baudrate device, the low baudrate device might consider it a valid transmission and start displaying garbage.