I don't have a curve tracer nor a variable DC power supply.
I know that the network already has a varistor(s), starting with the 425B network that was introduced in the early/mid 1950s (earlier model 500 phones with the 425A network used a separate filament-based "equalizer" to accomplish the same thing, i.e., make the volume the same regardless of your distance from the central office). The receiver element in the handset also has a varistor (originally the 44A in a metal can package with the U1 receiver, and later, a small plastic 104A with axial leads in the U3 receiver) to reduce the volume of any clicks/pops in the receiver.
I have another tone generator PCB in another phone which also uses a TCM5087 chip but has a different circuit design (picture attached below). It only has 6 diodes and only 1 of them looks similar to the mystery diode (small glass package). It has places on the PCB for 2 more diodes (CR7 and CR8), but they were left unpopulated:
Four 1N4004
One 1N5348
And unfortunately, its diode that looks similar to the mystery diode may also be a mystery diode. It does have writing on it, arranged like this:
SC
83
OF
But I can't find any relevant search results for SC83. The closest I can find is "HSS83" -
https://www.amazon.com/FFIME-Original-high-Voltage-Switching-HSS83TD/dp/B0CKB8QNSG