There is a lot of things left unanswered here in your post which is understandable for a pin repair guy/gal in training.

This would be a difficult measurement for anyone to make as it's hard to differentiate between a voltage measurement taken from the tieback voltage applied to the cathode of D16 (tieback) and the coild voltage applied to the anode of D16. With a broken tieback you will read very close to the same voltage on D16

The best way to verify this tieback is to disconnect J4 from the 8 Driver and check continuity from Pin 1 of the connector to the 50V test point on the power driver board.

I'm not sure this origin of this advice, nor do I agree with it as the pre-drive (Q8) is a signal transistor that carries no load and is also protected by D8; it's much more likely that a bad ribbon cable would causing Q8 to lock on, and damage Q16 vs a failed transistor.

Perform a resistance/continuity test to J4-1 as mentioned above, verify the ribbon cable is connected properly, try swapping the ribbon cable around on BOTH sides red line on the opposite side (J1-26) on both connectors to see if this has any effect.

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Actually there is, since the drive transistor is a darlington transistor, the metal tab is going to be connected to the transistors collector, . hen the transistor is on, the collector will be very close to ground potential and you can use this to your advantage fairly easily, all you have to do is follow a few simple steps:

1) disconnect J4 from the 8 driver PCB.
With J4 removed, the highest voltage on this board is going to be +12V.
2) measure the voltage between the 12V test point on the power board and tab of this transistor
If you measure 12V the transistor is locked on, if you measure nothing then its off.

Side note, a common practice for checking drive transistors this way is to use a 12 lamp and socket with one wire connected to the test point and a free wire to probe the transistors; this proves to be much faster than a meter when evaluating a driver board. This is exactly what I do when working on Fliptronics boards, I made a test jig with 8 LEDS on it and just connect it to the flipper drivers so even if there are shorted transistors, I cant blow fuses
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It shouldn't be related, but if you are pulling enough current on the 50V line to melt a coil, you may be seeing a sustained voltage drop to the other coils. I personally wouldn't address this until the known driver issues are resolved.

What were your results of this test?

Correct, if the Q16 was stuck on you would have measured 12V, the same as if measuring to ground. The tabs of Q9 and Q10 have 20V on them and you are measuring the difference between your 12V test point and the 20V on the tab, so these measurements seem fine to me. Q12 seems off but is not used in your game so I'm going to just ignore it.

If you are still melting coils and know the driver is not locked on, then the issue has to be in the wiring, perhaps a pinched wire providing a conducting path for the coils return wire (BRN-WHT); the next step is to check the resistance of this wire from the coil to ground (game powered off and J4 disconnected); you should be reading an open circuit here, if you measure anything else, you need to correct it.

Your ground checks seem fine, and if the coil is only locking on after the transistor fails then it essentially eliminates a grounding issue; in fact, your entire post reads just exactly like you are missing your tieback voltage and hammering the drive transistor with the coil flyback voltage making it fail...the problem with this theory is that to my knowledge you are ONLY seeing a problem with this one coil and if you were missing your tieback voltage you would be seeing multiple failures.

So we are back at a board issue with a possible bad flyback diode (D16), or broken connection to it on the 8-Driver PCB. You can verify these connection points fairly easily:
1) Cathode of D16 (striped side) to J4-1
2) Transistor tab to Anode side of D16
3) Transistor tab to J4-2
4) Anode side of D16 to J4-2

5) Diode test:
With J4 disconnected, place your meter on diode test, and with the black lead on the cathode of D16 and red lead on the anode, you should measure around 0.55V.

If all else fails you can always put a diode across the coil windings on the coil itself, but if you do this, you must observe the correct polarity with the diodes cathode (striped side) on the same terminal as the coils source voltage (violet/green) wire.

EDIT: Sorry, I forgot you had already done this

Sounds like you are all over this issue; to me, this really sounds like your flyback diode isn't in the circuit. I would make sure it is by removing J4 from the 8 driver board and measuring the resistance between the cathode of D15 to J4-1 this should be very close to 0 ohms and it should measure exactly the same as the cathode of D16 to J4-1. If D16 looks like its ever been replaced this would be high suspect as your 50V tieback on J4-1 goes directly to D16 in the topside of the board then feeds through a via at D16 to the bottom side of the board for D13-D15.