The printer and LCD do not send any data back to the CPU. If I leave their TX lines disconnected and only connect their RX lines that part of the problem would be solved.

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?

Here's an off the wall idea.
Some of the port pins are used to bit bang into a row of serial OC drivers and the other bit bangs into a EEPROM.

I could add another RS232 chip and some glue logic to use this clock signal whereas when the signal is high it switchs the glue logic to one RS232 chip input and when low sends data to the other RS232 chip. A chip for the LCD and a chip for the printer using the same TX from the CPU. The clock is not used when communicating with the printer or LCD.

Would that idea work?