There are several readings from earlier that are confusing. I think many are due to how they are being measured.

But based on latest info:
If TP4 is correct then don't mess with the 5V regulator circuit including Q3.
Note that he is not a standard transistor, he is a "Darlington Pair" transistor which has two transistors in the package. These do not test the same as normal transistors do.

TP1 -- you need to measure the 'setting voltage' which can be found at location "E2".
Meter grounded to TP3 - what voltage do you get at "E2".
It is a little high but not horrible. About 10% out of whack when it should be closer to the 5% range.

TP2 is fine. When you fix TP1 then TP2 will fall in line.
TP2 is calculated by voltage at TP1 minus 18V. You normally get about 60 - 18 = 42V. You get 68 - 18 = 50V. This says CR6 and R5 are good.

TP5 is bad. Replace CR7 and R10.

Out of curiosity: meter grounded to TP3 - what voltage do you get at "E4"?

SCR1 and IC1 have nothing to do with the 8V. These are part of your 5V supply which is working.

ONLY CR7 and R10 affect the 8V offset back to the transformer.
If you have a bad solder joint or cracked trace - that can be an issue. So can a mis-pinned plug on J1.

With meter grounded to TP3. Measure your voltage at E2 (for 62V supply) and E3 (for 8V supply).

E2 is high, E3 is low.

E2 is established by CR5 and R1.
If resistance in R1 goes too high, there will be insufficient current and CR5 won't conduct.
Check solder job on R1 and CR5 again. Check R1. Also possible CR5 can be damaged during installation.

E3 is low and may be due to low incoming 12V. With a 680 ohm resistor on input, the voltage drop across him my be too great and not allow the zener to hit knee voltage. We need to get voltage at E4 up before worrying about E3.
First step is to follow the voltage back to the source.

Going by your "Power supply/sound board: 16.7v" mentioned in last post. Assuming they share the same unregulated power - this says there is 16.7V in base but 9.5 at power supply. Screams bad connection if true. Voltage at E4 is labeled 12V DC but can often go a few volts higher (e.g. 16.7) with no problems.
At the black cap with screw terminals as shown above -- measure the voltage directly across the screw terminals.

One thing at a time - worry about lamp and solenoid voltages after you get the main 5V and display power up.

that's the biggest downfall of the gottlieb power - having to remove the transistor to do any other work.

571V? Huh?

What are you using for a meter?

Don't worry about R10 right now.

A fuse is a dead short and you should never see a significant voltage drop across it.
If you have a voltage drop across a fuse holder then the fuse is bad or the fuse's connection to the fuse holder is bad.
What brand of fuse did you put in it? Is the fuse holder tight? Or is it too easy to pull/reinsert the fuse?

And are you sure the meter is saying 26VAC? Or maybe 26mVAC (0.026VAC)?

mV makes sense -- you're ok with low readings in the mV range.

That resistor I don't know.
For where he is located - I would say as long as you match the wattage and resistance then you should be fine.

For the transistor - you can do better.
2N6059 and 2N6284 are better than original replacements for the 2N6057.
Make sure to reapply new heat sink compound!

If they work - leave them alone. They can last decades longer.

Think of a capacitor as a short term battery. In an overly simplified explanation, it charges up to a voltage while machine is turned on and drains down when machine is turned off. While turned off, the new cap is holding the charge long enough to light the LED but will discharge quicker as you attach other loads to the power supply. This shows the cap is working properly. Don't worry about this - it's normal.

For the solenoid and lamp voltages - DMMs often give phantom readings on low load sources. Only way to get a sure measurement is using an OLD needle type meter.