I may be having a foolish moment, and I was!
Usually try not to use both hands to avoid yourself becoming the path to ground

AC isn't referenced to ground. While that may work for some circuits, the correct way to do a voltage test (see diagram) is to put your meter in AC mode, touch one lead to transformer 8, and the other to transformer 10 - you should get around the 173 vac shown. (Sorry didn't draw the green box to include those terminals).

You of course have to have the input terminals powered up, see the note in the left corner.

It is most likely that one of the jumpers connected to the rectifier is not connected in the correct spot. Transformers truly, truly, rarely fail. And you will know it when they do, either because you will see smoke, or smell them burning up. (Enamel on the wires really, really, stinks when it gets that hot)

Now, a raw voltage test does not 100% test the transformer. There's some kind of load thing that has to be put on it, John Robertson at flippers.com always goes on and on about how you need that to properly test the transformer. I'm not going to pretend to understand any of that.

So the correct outputs to test are:

tabs 2/6=solenoid voltage (input to the bridge on the rectifier board)
tabs 17/18=lamp voltage (likely GI)
tabs 13/14=switched lamp voltage (input to the bridge on the rectifier board)
tabs 15/16=logic voltage (input to the bridge on the rectifier board)

You can also see on the diagram (the full diagram is with your schematics in your manual) the correct routing of the wires from the transformer to the rectifier board. What pins on the rectifier board fried? 5 and 6? High voltage +185 volts to the feature lamp bus? Yuck if so.

For the OP did you try the original rectifier board when you got the machine even though it looked hammered?

xformer (resized).jpg

The blowout across those two pins means there was an existing short circuit right there that fused - likely a solder splash across the pins when the J3 header was originally soldered to the rectifier board.
I doubt this had anything to do with the transformer.

Thank you for the correction! I’m way too tired to think this through properly!

What kind of fuse do you have installed at F2 on the rectifier board? Because it should have blown.

Boy the separation between the traces to J3-8 and J3-9 looks awfully narrow..

If the original displays are still there I would use them provided they test ok. But you'll probably have to check the four diodes on the rectifier board for the high voltage circuit.

The original small bridge rectifiers are no longer available. I would keep them for another game with a good original rectifier board that has a blown bridge. Don't throw them out.
The footprint of the original bridge won't fit new kit rectifier boards that use the larger 35 amp bridges.

Should be a fast blow fuse, not slow blow. 0.75 amps.

It won't have damaged the HV on the rectifier board, rather the feature lamps and SCRs on the lamp driver board will have seen excessive voltage.

Ah, you meant the new burnt board.
I would clean up the burn spot and see if the board is salvageable.
Otherwise just test the bridges when you pull them. Bridges are basically 4 internal diodes. Presume you know how to test a diode? Compare readings against a new known good bridge. One leg is marked positive, the opposite leg is marked negative. The two other legs are marked AC.

Stern originally copied Ballys design. Bally realised the error and changed to a fast-blow fuse from Dolly Parton onwards.
The 1N4004 diodes used for the HV rectification will likely blow before a slow-blow fuse does.

DollyParton_RectifierBoard_schematic.png

Yes, 0.75 amp fast blow as standard for the high voltage fuse on rectifier boards. I ran a 0.63 amp fast blow fuse in a game for some months when I couldn't get fuses early covid. I should have tried a 0.5 amp fast blow. How many solenoid driver boards have you seen with the HV section blown out? Too many..

I'm running a 7 amp fast-blow in my Seawitch. Though it has four standard strength 25-500/34-4500 flipper coils all round. I suspect it will work fine with a 6 amp fast blow (like Bally specs for games with 4 flippers).
I don't have a 4 flipper Stern game with higher strength flipper coils on hand to test. I wouldn't be using 7 amp slow-blows on 3 flipper or less Stern MPU-200 games (unless proven otherwise).
I'd rather have a fuse blow than a bridge rectifier blow.

Unplug that board and see if the problem goes away.

With only J2 hooked up to the rectifier board, there is no downstream circuitry connected to the rectifier boards HV.
Sure you installed the four 1N4007 diodes the right way around?
How much AC voltage do you measure between the two 1N4007 middle traces (i.e. the transformer HV outputs at E5 and E6)? Schematics says 173VAC.

It's reading normal (I forget the exact but somewhere around ~160-170)

We're using the same boards we've used in countless other machines (any game we replace the rectifier board in). I did have these made myself but they've been working just fine until this game for some reason

Well with only J2 plugged into the rectifier board, there's only the four 1N4004 HV diodes after the F2 fuse. One or more of these diodes may be bad / backwards or there's something shorting the back of the rectifier board to the rear metal plate.
Test the four diodes with the rectifier board in place and see if you measure any shorts.