"without any high-tech equipment (beyond the usual ham stuff such as
resistors, VOM, etc.) how might those diodes be tested?"

You need to build a hi-pot tester. Schematics are found using a search
engine. Basically, you take a high voltage dc and connect it through a very
high resistance and a microammeter to the device to be tested. Then, you
crank up the variac to see when the device fails. Current will be limited
so you will not damage it.

You can use one of your discarded microwave units for the voltage source,
which means that you will be looking for a variac and a couple of low
current meters along the road to complete your test equipment wish list.

Colin K7FM