I find about half of all old CRTs don't have the right cutoff. I usually have to go to a lower bias voltage range. What I find is that even if I have to go to a lower bias voltage range to adjust the cutoff, if the CRT then tests good for emission, it works very well in a set. No obvious problems with greyscale linearity or anything like that. So I don't worry too much about what the cutoff bias voltage is.
So no need to "inquire" another tube.
