Hi Henry ,
Im not sure I understand your question . You say the unit will give up to -22 volts and the tube only needs -16.5 of grid bias , I'd adjust it for the -16.5 and call it good . You mention the instruction specifying -4.5 volts but it says that is for one particular tube type , the 201A or 301A , and that other tubes will use the value of grid bias as listed "In the instructions packed in each tube carton" .
A quick peek at the 71A's specs reveals that at +90V plate the bias will be -16.5V with 10MA of plate current flowing . You could connect a meter measuring in MA into the plate circuit and adjust for 10MA or less .
Interesting to note , the 71A can operate as high as +180V plate , -40.5V grid bias , at 20MA plate current . You'll have to stick to your +90V plate however , since the specs at even +135V plate call for -27V of grid bias , and your C supply maxes out at -22V .
PS , in the Atwater Kent drawing , they have the A- and B- strapped together with the green wire between terminals 2 & 3 , this is proper and is what I'm used to seeing . So why does the ARBE unit's drawings show the B- connected to the A+ ? I think I would connect it the way Atwater Kent has it wired .....