If you determine that one or both of the bridge rectifiers might be defective, you can get some here:
https://www.pinballlife.com/mm5/merchant.mvc?Screen=PROD&Product_Code=KBPC3504&Category_Code=
They are not very expensive.
Might as well replace them both.
You can keep one for a spare if they are both not bad.

If you are so inclined, you could post pictures of some of that special wiring that you encountered in this area:
https://pinside.com/pinball/forum/topic/worst-hackrepair-you-ever-saw
It will not be a really bad one, but it could qualify...

Yeah, that looks pretty nasty.
Perhaps those connections can be repaired.

Its rated 400V, 35A, so it is the same device.
They are pretty common.
I would not expect the photo to exactly resemble the device, but it is similar.

I would guess that if there was an actual short in the transformer, there would have been a rather violent reaction, like an explosion or fire, or at least a blown 120V fuse on the input to the transformer. A problem with a bridge would create high current that would cause some heating in the transformer and possibly a buzzing sound. I think that is what is happening here, given the information that we can see at the moment. The same affect could be possible with a bad/damaged wire that has created a high resistance path to ground. My guess is that if the lead connections can be repaired, that the transformer is still ok. Some problem (like a bad bridge rectifier) on the low side of the transformer has caused it to get hot or buzz.