[Electronic M]

Purity rings behave the same as centering rings on a monochrome TV...If there's only one tab on each ring then when the rings overlap they cancel each other out and at maximum spread have maximum shift in one direction that you can rotate by moving both rings at once in the same direction.

If you can get a service degaussing coil or make one from a scrap BPC TV (as I have a sticky on somewhere here) it's a good idea to manually degauss before going through the purity process as sometimes the screen can get magnetized bad enough that the internal degausser isn't sufficient.

If yoke travel is limited and you can't get good red spot, adjust for best centered red you can slide yoke forward until the screen isn't underscanned and you find the spot with minimum impurity (it doesn't need to be maximum forward in operation), then if necessary tweak rings to eliminate or minimize impurity.
I've had at least couple of sets where yoke travel made the by-the-book purity adjustment process impossible (was able to get through it by feel and screen educated guess work)...If there's bad enough screen magnetization you'll never get it perfect or have a very long manual degauss ahead of you...Some sets only need a degaussing.

BTW you can undo some angle braces at the sides and hinge the chassis down and away from the CRT to get better access if necessary.