Found an Eames LCW. Want to repair it, but should I?  

Well, I think I can answer at least one question. I did a little glue residue removal and took the chair apart this afternoon. The back wood screws, which I interpreted to be black based upon online photos and previous quick glance at my chair in poor light, are actually stainless steel after all, with a dark corrosion patina exposed head. I guess the SS alloy used for the wood screws was different than the one for the dome screws, resulting in greater corrosion of the former. So the Evans chairs which look like they have black/dark rear screws probably spent some time in the garage, attic, etc. during their lives, while the more silvery ones were better cared for.

Are you sure about stainless steel? Both the flat head wood screws and the truss head machine screws in your pics appear as standard zinc-plated steel to me. I've darkened the heads of zinc-plated screws with cold gun blueing solution on a few projects and they came out looking pretty much exactly like yours.

Merry Christmas, btw. Great chair, too!

Well, now I have been wrong twice about these screws. I believe you are correct, tk; they are zinc plated steel screws, not stainless. I guess I looked too quickly once again, and they did not immediately match the galvanized screws I see at HD these days. So a little Google just now helped educate me on zinc plated (hot dipped) versus electro-galvanized. Also, there was a little “white rust” on the screws and nuts, which I had previously not paid attention to, but is a sign of zinc corrosion, not ss. Whatever the exact galvanizing process options were back in the 40’s, it does appear that the two different screw types used different processes.

thanks for setting me right, and Merry Christmas to you as well.

P.S. two nice videos I found online which help confirm early Evans chair screws were all Phillips head. In one chair, which seems to have been pristinely kept, all screws are still shiny. In the aniline red video, those wood screw heads are the same color as mine, indicating more exposure to the elements. 
https://youtu.be/uPE7aZQNBro
https://youtu.be/UcaH359CYxk

... and speaking of red aniline dye, I just came across this oldie but goodie thread. Too bad the OP’s photos are long gone (one of the biggest travesties of the website format shift a few years ago).

http://old.designaddict.com/forum/Repair/DCM-Stain-or-dye

For a couple of years, I had a photo of that sanded DCM seat hanging up in my basement shop as a constant reminder not to shoot first and ask questions later.

Aha. This version still has the photos 

https://designaddict.com/community/repair/dcm-stain-or-dye-/

I'm an idiot. This chair is a DCW, not LCW. I made an assumption from the initial photos that the seller sent, and was too busy looking at details when it arrived to notice the overall dimensions. I noticed today as I was cleaning off the old shock mounts and thought to myself "Gee, these legs are kinda tall for an LCW" 🙂 

I hate when that happens!

P.S. I'm laughing with you, not at you.

Well, I was laughing at myself so no worries there. I knew there was a reason I normally stick with Danish.

Since it was a last-minute throw-in for a very good price, I'm still happy. And the seller didn't claim it was an LCW either, just some type of Eames chair. 

I'm also happy I figured it out before I ordered the larger LCW oval shockmount from Special K.

... and, at least I'm not alone!

https://designaddict.com/community/main-forum/eames-lcw-molded-playwood-chair-age-type-of-wood-value/