Turn off all loads on the circuits in question.
Turn off the main for this panel. Possibly overcautious, but that's part of what's let me get old.
Either: short the dead circuit, or turn on an incandescent bulb on it (main off, circuit dead, still dead - just the bulb/fixture/lamp turned on.)
Pull neutrals and look for one with low resistance from the hot in question. There should be only one. Unshort the circuit or turn off the lamp and make sure the resistance changes (if nothing else is turned on, should be infinite, but if there are things that are not able to be switched off, may be non-infinite. But you should see a difference when you switch the incandescent lamp off or remove the short - it's a form of verification.
I think you have enough neutrals not to worry too much about this, but: beware of "Multi-Wire-Branch Circuits" where one neutral serves two hots.
As for the wire colors, only white and green (with or without yellow stripe) are reserved (and IIRC, you can retag white to another color, but you can't retag green - and you can't retag anything else to white.) If your wiring is run in conduit, using the full range of available colors makes figuring out (what is connected to) the hot side of circuits much, much easier. Most household wiring is not run in conduit, so it's not often seen at home.
The ground conductors were probably functioning as your neutral return (just not very well) until you disconnected it at the light. So not only do you have an open (or high resistance) neutral wire, but you also have too much resistance in a ground wire. If you've checked all the boxes and terminals for loose connections, you may have a damaged wire in the structure somewhere. The high resistance will cause heat (and risk of fire) if you continue to use the circuit. I would probably contact someone who has access to test equipment that can diagnose the actual in-wall wiring. (like maybe an infrared thermometer to detect a hot spot, or a voltage detector to trace wires in the walls, or at least an ohmmeter)
Best Answer
Some things don't make sense here. Standard low voltage transformers should have a hot, a neutral and a ground wire. They are single phase and should be installed into the side of a standard junction box through a 1/2" knockout. Then you just match the wires to the circuit wires. The low voltage connections are then on the outside of the box.
Low voltage transformers aren't normally attached to the main circuit panel since their wires are usually too short to reach the connections. There is nothing in the Code saying you can't, you might just have to extend the wires.
Even in 1960's, houses in the US were built with split phase three wire services. The main panel would have two hot legs attached to the breaker bus bars a neutral and a ground bar. At the main panel the neutral and ground wires can be mixed on the same bars. If you choose to attach it to the main panel, the neutral and ground wires should be attached to one of those bars.
The National Electrical Code prohibits the use of course-thread self tapping screws for ground connections. The threads have to be fine enough to engage a minimum of 2 threads in the material of the enclosure. See 2017 NEC 250.8(A)(6).
Good Luck!