PAGE and HIMEM are what you might call "system variables" in BBC basics, they mark the bottom top of the memory available for Basic use, they are intiialised from OS-provided values but can be changed by the user.
On a regular BBC micro HIMEM will point to the bottom of screen memory, so it can change if you change screen modes (this BTW meant you couldn't change screen mode within a procedure, because the procedure stack grows down from HIMEM), but on a second processor it should always point to the bottom of the OS unless it is manually changed.
So what I would do if writing a ram tester is manually change HIMEM to give my program a small workspace, the program can then test the space between the new HIMEM and the old HIMEM without worrying about being stepped on by BASIC. If you are using regular Basic you can also test the area between BASIC and the OS.
For testing the area with BASIC in it you could just run a checksum and compare the results running it on the copy of BASIC in the second processor to the copy in the machine itself.
Not sure of any easy way to test the OS code area at the top and the workspace areas at the bottom.