I have measured the ohms on 2 of the pots and I get absolutely no change in my reading. I'm not meaning to rush into anything, I just figure while I'm tracking down new pots I may as well give it a capkit so that I take out two possibilities at the same time.
This might just be because of your measuring tool's sensitivity setting, or perhaps because there will be no change because of the ranges set somewhere else on the monitor.
Don't rush into changing the pots either. I think you are making unnecessary work & stress for yourself. Dodgy pots are more likely to be loose and/or be 'crackly' when you adjust them. Sony pots are a bit stiff so that they don't move accidentally - this is normal. Use a good tool and a firm but gentle hand.
Considering that you have used these in your projects, what would you recommend to possibly make the convergence a little more clear, and some waviness in the corner a bit better.
I haven't managed to track down schematics either. I have used the Sony PVM2730's before, which should be very similar. There are a large number of pots for making fine adjustments on the back and left side (right side if looking from the back). These can be used to make some fine adjustments to your convergence ("dynamic convergence"). However, they don't really make any difference to the visible screen size. You might be able to improve the "waviness" that you talked about, but I can't be certain.
Make sure that you mark the original positions of the pots, and adjust them one at a time. If you can't work out what one does, make sure that you return it to its original position. Some pots will not give a visible result. You may need to adjust more than one pot to get the changes you want.
For more serious convergence issues, you need to look at adjusting the yoke and/or the multi-pole magnets (the cluster of rings) at the back of the CRT (this is the "static convergence"). I wouldn't rush into this either as it is a pain in the arse. With the Sony PVMs, there are multiple PCBs and the boards are clustered around the back of the yoke, making this an even bigger hassle. Avoid if possible!
What is the "waviness" you mention?