What type of transistor did you replace Q35 with?

Can you post a picture of the solenoid driver board (SDB) around the Q35 area, and if possible the back of the board where Q35 is?

MPU board U11 is just an I/O interface chip. There is no internal code in it. You can swap it around with U10 to help diagnosis.

Your problem is more likely around the U4 transistor array on the solenoid driver board. What voltage do you measure on pins 4 and 6 of U4 on the SDB?

Nothing out of the ordinary in the pictures.

How did you go taking voltage measurements of pins 4 and 6 of the U4 chip on the solenoid driver board?

BTW, don't bother bending the transistor leads over when soldering them in, it only makes life harder next time you need to remove them adding to the risk of damaging the solder pads.

When input pin 6 of U4 is at zero volts, the downstream result is that transistor Q35 will switch on and activate the solenoid connected to it.

Can you:
Power off the game.
Disconnect the J4 connector from the solenoid driver board.
Power on the game.
Wait till the game gets to attract mode (note: no lamps on the playfield will be on) and remeasure those two pins (6 and 4) on U4. Let's find out why pin 6 is at zero volts.

Pin 6 should be near 0.8 volts resulting in pin 4 being near zero volts for the solenoid to stay off.

5 volts at pin 6 of U4 on the solenoid driver combo board means that U4 chip has failed. Pin 6 should never go above 0.8 volts and in your case it has internally gone open circuit. The result is that pin 4 is stuck at 2 volts which is constantly activating transistor Q35 and that coil.
You need to replace that U4 chip. It's a "CA3081" transistor array chip. Good luck!

The schematic doesn't show any use of the internal transistor at pins 11 and 12 of U4, so the connection between pin 10 and 11 was unlikely to have caused any issue. If you're saying it was a solder bridge between the pins, then I wouldn't be soldering those legs together.

Downstream from pin 10 of U4 is the open gate coil driven by transistor Q36.