...At the moment I can't think of a method of doing a back up of the OS 7.5 before installing OS 6.
There's another way to do this.
Boot from a System 7.5 floppy and open the "System Folder" on the hard drive. Create a new folder there and drag the file "Finder" into it. You can call this folder anything. I usually call it "Finder Disabled".
😉
Now, again on the hard drive, create a new folder and drag "System Folder", "Applications" "Documents" and "Apple Extras" into it. These are the folders that are ALREADY on the hard drive.
Now boot up from a System 6 install disk, select the internal hard drive and install. You will now be able to boot from System 6 using the hard drive.
To re-instate the System 7, perform the above steps with the System 6 "System Folder", disabling the System 6 Finder and drag the System 7 items back to the root level of the hard drive and finally, put the System 7 finder back in it's original location.
What you're doing here is resetting the "System Folder Pointer". Behind the scenes, when the computer wants to boot an OS, it looks at the system folder pointer which tells it which folder number (yes, they're numbered) to find the System file.
It can get a little scary, but this does work. I always disable the current System First and move it's location otherwise the System installer will either follow the "blessed" system folder if you only move it or it will over-write items in the system folder of the same name if you only disable the finder.
A System Folder that is not blessed won't have the MacOS icon on it. One that IS blessed will have the icon. (I suspect this only applies to system 7 and higher IIRC).