You could redesign the circuit to use TTL (assuming the Fairchild chips actually turn out to be a problem,) but you're not going to be able to simply plug some other ICs into those sockets. The TTL analogues to the 946 and 960 would be something like the 7400 and 7441, but the pinouts and logic levels are going to be completely different. The only 1:1 replacements for those chips would be the exact same part numbers. Anything else and you're going to have to design and fabricate a new logic PCB.
I can't see from the diagrams where the "B" and "C" inputs to the LFO board are coming from, presumably on the PSU somewhere? A clearer shot of the PSU diagram might help. It would fit the symptoms if the 12VAC isn't getting to the LFO board.
Anyway one thing to always check with old kit are any plugs and sockets, it looks like the vertical board to the right (proably the LFO board) is connected by a blue PCB edge connector. It would be worth carefully pulling the connector off (having noted which wires are at the top), checking for corrosion on the connector part of the PCB, cleaning gently with fine abrasive like a brass or glassfibre brush and refitting it. Or just plain removing and refitting it a couple of times. Don't do this with the power on!
The ICs all appear to be socketed too, I've often found that the IC legs on really old kit go black and benefit from attention with the glass brush, just do one chip at a time and be sure to put them back the same way round you found them!
any updates? I think we would all love to see the clock back up and running.
ran into any troubles you might like to share and see what the group thinks?
(just for full disclosure, I actually work with Nixiedave at the same company, though in different departments and different stabte. I haven't talked to him for a bit.. but I was wondering how he was doing with his clock).