"Completely different processors"
You may have to have two different kernels because the kernel has different code for AMD, Intel, etc. but not different code for different speed processors by the same manufacturer.
You can set up two different copies /etc/X11/XF86Config and copy the correct version to /etc/X11/XF86Config with a script in /etc/rc.local. /etc/rc.local is the last script run at boot. In /etc/rc.local you could test the results of a uname command to find out what kernel you are running and then copy the corresponding XF86Config file to /etc/X11/Xf86Config.
This configuration might work where you have one Linux system with two kernels and two /etc/X11/Xf86Config.
Looking at the two system solution:
"So basically, what you're saying is that I have to install linux again on the same drive to another partition?
I can't quite do that, since it's a puny 4.3GB drive, all in one partition, with Red Hat 9 taking up about half of that."
You can save space by having the two Red Hat systems share a /usr partition and a /home partition. /usr takes about half the hard drive space in a Red Hat system. As long as both Linux systems use the same version of Red Hat then they can share /usr and /home OK.
Be prepared. Create a LifeBoat CD.