Well, I had a second electrician and opinion here this morning. I expected nearly the same with a few variances from the first electrician. Wrong. He was almost the exact opposite. I'll list the individual topics with their answers side by side. I'll list the newest one as "B" and the one from Monday as "A":
Shop breaker box?
A and B: Change it! Your selected box is just fine.
Compressor/starter wiring?
A and B: It's lazy work. Fix it.
Do I need redundant breakers for the shop at each box?
A and B: Yes.
To answer ABN_CBT_ENGR's question - Is the 125A "main" box being supplied 125 amps?
A: At least that, if not double.
B: Yes, but you should be asking what is coming OUT of it instead.
Should I replace the "main" breaker box? Is it overloaded?
A: No and no, but upgrade the shop breaker to 100A.
B: Unquestionably yes and yes. It's the single largest problem. You need a 200A box.
Is the overhead wire between the pole and shop in need of replacement?
A: YES! It's worse than any I've seen.
B: No, it's not going to help anything. There's nothing wrong with it.
Does the compressor receptacle/wiring/circuit need upgraded?
A: No, the other issues will fix it, this setup is just fine.
B: Yes, it needs AT LEAST 8AWG and a 40A breaker. Get rid of the receptacle and direct wire it.
Is my proposed ground rod setup alright?
A: It is perfect.
B: No. You can use this setup at the shop, but you also need two at the pole. One for the house [to supplement the existing one] and another for the shop. Two grounds are [supposedly] required per code.
Good grief. Talk about a mixed bag of answers. I'd love to hear what you all think. I'll get some pictures of the overhead wire later to help form opinions.
Oh, and electrician B said: "I think you need some more oil!"
And he would be right!