Awesome, thanks for the information everyone.
I looked through the rest of the schematics, and found regulators for 15V rails, but they're marked as +15V2 and -15V2, rather than +15V1 and -15V1, which is what is connected to the zeners. Here's that circuit:
I buzzed it out to be sure, and it doesn't appear to be the same 15V rail connected to the zeners. I'd kinda like to know if salbayeng is right about the zeners protecting the regulators/helping them start, or if they're meant to provide a voltage rail (or both?). Here's the rest of the bias supply circuit:
If this is the wrong thread to ask that, then I apologize, and you can disregard.
In any case, I guess it's somewhat beside the point. I'll see if the 2.4 V zeners I've got in there are within Agilent's specs, then whack in a 5.6 V and see if that's better or worse. At least now I know I need a 1 amp zener.
Thanks again!
EDIT: I borked it and shorted the diodes together, because I'm good at what I do.
Also managed to lift a trace in the process.
Going in for emergency surgery. Guess I won't be selling this one.
EDIT2: Voltage regulators on the main board check out OK. No display with two beeps means it can't communicate with the display board. Probably blew a regulator local to the display or PC board. Will test those and try to hot glue the lifted trace down to prevent any further damage.