Jimmy's #1 doesn't have the complicated wiring. Just 50's with a mod to the bridge pickup. The wiring scheme that he's now known for didn't happen until way into the 80s. Well past any Zeppelin stuff. If it was me I'd buy a regular Gibson sunburst Les Paul and change the pickups and wiring to normal and be done with it. Brandonwound pickups make an excellent JP#1 set. Email them for the proper wiring of the 70s. I'm not sure I remember correctly. I can't see a reason to drop that much cash for his signature especially if you get a custom shop 50's. Buy it from Wildwood guitars or the Gibson Garage as you're sure to get a good one and could return it easily if youre not happy. Wildwood guitar shop is particularly selective in their guitars. Unless you have the money for a JP signature. Which certainly would be great investment as well as bringing you great pleasure. I think Jimmy's #1 is a 1958? No matter, they have 1959's. On this site you can see all their guitars. Plus you could call and ask which one is like Page's. Here is just a random example. These guys are pros and have their guitars personally made or selected by Gibson. They also have just the regular American series which is cheaper but im sure you could have one picked to look the same as Jimmy's.
https://wildwoodguitars.com/product/82110/wildwood-spec-1958-les-paul-standard-light-aged-6/?cat_id=21825