There in an extra LVDS channel for 24 bit (vs. 18 bit). The majority of displays run the extra LSBs over the extra channel, but there are a small number of displays that run the MSBs over the extra channel. This means in most cases you leave the software in 24bit mode and an 18 bit panel just does not have a receiver for the extra LVDS channel. No hardware changes required.
Your real issue is likely because the AM335x is screwed up in that the bits are swapped between 18bit mode and 24bit mode, this is a silicone error. So when you set the software to 18 bit mode with a 24bit hardware layout, colour bytes are inverted. Try keeping the software in 24bit mode and connect the 18bit panel, it should just work. There is zero chance of damage (unless the LCD connector pinout is different, or power supply spec is different, etc.).