Here's another way to look at it from a schematic perspective. The schematic will show you how it is supposed to work.
We know the special becomes active when all targets are down and all letters are activated.
That is two different circuits, targets and letters.
I assume the machine works properly when
(1) All targets are down (double/quad score works)
(2) All letters down feature for the extra ball works.
(3) The machine adds credits properly in all other instances, such as high score or adding coins.
(4) The ball ejects from the hole when Extra Ball is lit, but does not award an extra ball. (I am guessing that's the case)
Since those three modes seem to work, we can pretty much eliminate much of those individual circuits. The question becomes what is the common circuit to all three. It can get confusing to look at the whole picture, we need to narrow down the possibilities and save troubleshooting time. One way is to consider logical inputs and outputs.
In this case there are two inputs (Targets and letters) and one output (Adding credits).
Since there's less outputs than inputs, the trouble may be easier to find by considering the output. How it adds credits.
We look at the schematic and locate the "Add Replay Unit" coil. It has a lot of connections to things we know already work, such as score reel circuits, coin circuits etc. If we look around we find the connection I drew in red on the modified SO76 schematic. A good hint is to consider it's from the Add Replay coil and goes to the drop target circuits:
We see it leads to the 1776 and 1976 drop target switches, which we already know is working. Notice the red branch goes through three switches. 6B which is the Sequence Completed Relay, the Bonus Unit Score Control Relay (J) and a score motor switch 4E.
Relay 6B is located in the middle of the relay bank under the PF. It does not have a trip coil. It is instead mechanically linked to the other relays near it, so when the surrounding relays for rollovers A-E are tripped, the Sequence Completed Relay "trips". If that makes any sense.
The circuit in red also goes through Relay J and Score Motor 4E. The Score Motor timing chart shows that 4E closes just after it begins to rotate.
This means all 3 switches must be closed to activate the Add Replay Unit coil, adding a game.
The way the hole special circuit works:
(1) We can see that all targets down close the 1776 and 1976 switches.
(2) 6B closes when A-E is made
(3) Current goes through the Score Control relay (Which prevents a free game from happening every time the score motor operates).
(3) The Add Replay coil is pulsed via Score Motor 4E.
Since mechanical things will usually fail (Old grease, bent etc) before electronic stuff, the first suspect is the Sequence Completed Relay under the PF. Check to see it really mechanically trips all the way when relays A-E are made and all the switches on it have been cleaned with a fine metal file and correctly gapped.
--> Make sure the relay bank is secured to the bottom of the PF via the two end mounted wing nuts, that it is not swinging loose when you work on it.
If that doesn't fix it then do the same with the Bonus Unit Score Control Relay switches.
If that doesn't fix it then do the same with the switches on score motor stack 4E. Keep in mind there are120v line voltage on some score motor switches so work with it unplugged.
I know this is an overly complicated and long post for this issue, but maybe it might help someone understand a way to look at schematics.