Sounds like capacitor C23 on the solenoid driver board isn't functioning either due to failure or probably because its negative lead that connects back to the rectifier board has lost connectivity. Check the wire terminals of the white-brown wire at pin 10 of J3 of the solenoid driver board and pin 17 of J3 of the rectifier board. Re-terminate if either are bad.

As extra redundancy there's some mods for the solenoid driver board which one caters for this weak point:
http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#Solenoid_Driver_Upgrades

Using your multimeter tone as a guide for continuity can give you false readings. Multimeters will give a tone sound even when there is up to 150 ohms of resistance. You need to set the multimeter to resistance mode and look for zero ohms readings when checking continuity.

The voltage at TP3 on the rectifier board (with the head (J3) disconnected) looks like point Q below. When you connect J3 to the rectifier board and it applies capacitor C23 from the solenoid driver board onto the 12V supply rail, it will now look like point R. That capacitor stores energy and raises the average voltage on that supply rail. Since you're getting a low voltage there, it looks like C23 is not connected or faulty so is unable to filter that 12V supply rail which is causing excessive ripple on the input to the regulator. The ripple is causing drops to zero volts during the voltage phase (as you see in point Q) resulting in the regulator output being low. The voltage regulator needs a voltage on the input that is at least 2 volts above its output voltage rating and it must never drop below this in order for the regulator output voltage to be stable.

Even if C23 was properly connected and working and you were still only measuring 10 volts, it's still a high enough input for the voltage regulator to output 5 volts.

If you disconnect connector J3 from the rectifier board, what voltage do you measure at TP3 on the rectifier board?

Voltage_WaveformsA.jpg

That pretty much tells me the problem is around capacitor C23. A functioning C23 capacitor will bring that 10VDC up to just over 14VDC as it removes most of the ripple and flattens out that supply rail.
Another way you can check is to measure the AC voltage at TP3. If it's around 10 volts AC, then C23 is not filtering that supply rail. If it's around 0.2VAC then C23 is doing its job.

I'm big on diagnosing faults before replacing parts. Measure the voltage directly across the legs of capacitor C23 - black meter lead on the negative capacitor leg, red meter lead on the positive capacitor leg. If you measure 10 volts, then the capacitor is connected in circuit but has malfunctioned - would be strange for a cap that was replaced a year ago. If you measure substantially less than 10 volts there is an open circuit (probably ground) to the capacitor.
You can also do the AC voltage measurement I just mentioned in the previous paragraph.
For reference, the ground mod for C23 can be seen here in @vid1900's guide:
https://pinside.com/pinball/forum/topic/vids-guide-quick-bally-driver-board-repair-bulletproofing#post-592759
The other two recommended mods for the solenoid driver board are shown around that post.

Just note, with electrolytic capacitors, smallest physical size does not equal better. They overheat quicker which results in shorter life span.

Check the 1 amp slow blow fuse under the playfield near the flipper mechs. That fuse is for all the playfield coils *except* the flippers.

BTW, I use a 15,000uf cap at C23 on the solenoid driver board too.

You've got suspect power stability issues with that Meteor right? What's the chance the MPU locked up and a coil locked on? Is there any suspect wiring on a coil? Did you notice what the last solenoid was that activated around the time the fuse blew and all other coils stopped working?