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Nope, right area of the forum and welcome.
Can't see any obvious errors and it looks to me as though it should work as you describe. Just one point to note (which you may already be aware of), as you are wiring the pots "back to front" for left hand use and assuming they are log pots they will...
I assume you mean output jack (guitars don't have input jacks!). I'm not quite sure what you mean by a "hat" (pictures would help) but 70's Gibsons typically had a metal shielding can around the jack, the shielding can is in direct contact with the jack socket body so needs no additional ground...
If you Google "Grover Deluxe Tuners" you should find them, they look exactly the same as Kluson or Gibson deluxe tuners except that they have Grover Deluxe stamped on the back (pictures show up fine for me).
Not really sure what you are asking here as you don't say what you are connecting to the CD changer input. The chip you linked to is a digital to analogue converter, not an op-amp.
In any case a guitar forum is unlikely to be the best place to get answers to questions about car audio equipment!
Perhaps instead of obsessing about details or worrying about which years the internet "experts" tell you should be avoided you could try playing the guitars and pick one that you like - a radical suggestion I know but it might just work!
It's very simple to try both ways to see which you like, you only need to move 1 connection to change between the two. It makes no difference which way the tone pot is wired, it can be wired either way round, the only thing that needs to be changed is which lug of the volume pot the capacitor...
The capacitors are ceramic disc caps not orange drops. Gibson were using ceramic caps on SG's in the early 60's so doesn't help much with dating. If you can read the numbers on the pots (can't see them clearly enough from the photo) that would make it possible to date the pots at least.
It's unlikely (but not impossible) to be the cap, guitar capacitors rarely fail as they are not subjected to any voltage, much more likely to be a wiring / solder joint problem or a faulty pot. Try checking the pot resistance between the lug that the capacitor connects to and the grounded lug...
As I said previously, due to the fact that gold plating is very thin (typically less than 1 micron) the cost of the material used is not overly significant. It costs only slightly more to electroplate something with gold than it would to electroplate it with chrome or nickel.
If you don't believe it is gold plated then I suggest you contact Gibson and ask them but I can assure you that the answer will be that it is. The Gibson website lists the pickup covers as being "Gold-plated Nickel Silver". It would be illegal to claim this if they were not!
An operational amplifier, more commonly referred to as an op-amp, is an integrated circuit chip that contains a voltage amplifier circuit.