Is it possible to nudge automation vertically (change the value) with a key command? Horizontally works fine, but vertically doesn’t do anything.
'fraid not.
But you can select the automation and change its value by using your scrollwheel in the Info Line 
Make a Logical Editor preset and assign a Key Command to it.
It wouldn’t be quite the same thing as Nudging though. The Project Logical Editor can scale the automation values (Trim>multiply/divide) but cannot simply increment them.
Yeah, but multiplying by .01 or the like is the same as nudging, no?
To our human ears, certainly! I was more concerned that, when de-crementing, dividing by .01 may not return exactly the same value, because of rounding errors (although, I must admit, I do have two PLE presets for that very function myself . Btw, in practice, .01 makes hardly any significant difference, … I eventually settled for “Multiply/Divide by 1.1”)