If its not already done, you might shunt all ground white wires on top left of the tranformator as it is preconised on pinrepair.com

Here :
http://www.pinrepair.com/sys3/

I'm pretty sure the problem came from that cause I've never have any Mosfet burns after I did the ground upgrade.
You might done this first before check anything

As you can see on schematic there are 2 transistors legs shunt together and link to the capa directly...also every components (capa, transistor and resistance )are the same on every solenoid lines so follow and check a working line (values between every transistor legs in both way +- & -+ on multimeter and compare it to the non-working sol. line...you might have same values everywhere and also test every lines of sol. 3
If you change transistor be sure that you got an IRL and not an IRF.
When IRL burn it also burn A3 board that's why there are shunts on the back (bought my stargate with and add some after many irl burns... I shunt all ground wires and now works pretty well since 8 month...another one burned but it was because a motor broke without protection between it and A3 so I add a fuse after replace the motor...all works now...for how long)

Quote: pictures cames from www.pinrepair.com

And take your time by checking the most you can.
Have fun

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So check if there is no shunt between + and ground, unsold coil and put your MM on Ohmmeter then touch wires...nothing might happens on Ohmmeter.. if it ring or show a value between 0,1 to 1 it's bad

I think you already unsold coil and test wires ohm value...

Also did you disconnect mechanical parts of these sol2. coil?

And follow all common wires links to sol2 under your playfield to find a potential unsold wire...

Not sure...fuses are here to protect transistor board so I think if there's a short after fuse, only fuse will burn also when there's no coil soldered.
But test if there is a short between orange black and +48VDC top fuses sold together but probably nothing...the problem is probably that the signal black orange is cut somewhere (but I don't think so because Q3 might not blow) OR the ground on Q3 is cut somewhere
Also test the red mark I made on schematic, put your test pin voltmeter directly on the board near Q3 and the other pin to A3P7 ground connector on A3 and also follow those ground wires to the top

Good luck
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Did you check volts coming to coil wires without sold the coil on them?