have you tried removing J1, J2 & J5 then turning on the game and seeing if the fuse goes open?

these 3 plugs are all your solenoids

another way to test for an internally shorted transistor is, with the game off, your meter on continuity/lowest ohms/beep setting, put either probe on the metal tab of the transistor, the top piece usually with a hole in, and the other probe to ground (you could slide it under the ground braid where it joins from the playfield to the backbox), listen for a sound touching each metal tab. If you hear a sound/see zero ohms resistance then that transistor is faulty.

check the switches on your right sling shot, and also the diode on the coil, and the resistance of the coil.

you will need to remove either wire to check the resistance of the coil.

Personally I reckon it would be a shame to not give replacing U3 a go.

That's a real tidy Solenoid Driver Board.

As above, if your running gas displays replace both the big blue electrolytic capacitors and do a couple of ground mods and TP1 to TP3.

Good Luck!

There's 2 ways to go, there's 'if it ain't broke, don't fix it' & there's also taking it's age into consideration and she may need some more tending to that will only keep her in peek playing condition with peace of mind.

IMO it's enjoying and relaxing rebuilding mechs and replacing worn parts to then put it all back together.